Trigonometry Questions and Answers

St 23 to y sin x Oy cot x 0 The graph above is a graph of what function Oy csc x Oy tan x Oy sec x O y cos x

A point P x y is shown on the unit circle corresponding to a real number t Find the values of the trigonometric functions at t The point 5 245 5 2 5 P is sint cost tant csct sect cott P point s possible Q Q 1 0 C Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression

A ladder leans against the side of a house The top of the ladder is 24 ft from the ground The bottom of the ladder is 10 ft from the side of the house Find the ength of the ladder If necessary round your answer to the nearest tenth 24 10 0f

Sive a pair of corresponding angles a pair of alternate exterior angles and a pair of alternate interior angles 8 6 4 2 57 13 M a Corresponding angles b Alternate exterior angles c Alternate interior angles X and 0 and 20 20 and 20 N S

Give a pair of alternate interior angles a pair of alternate exterior angles and a pair of corresponding angles m 4 3 2 18 1 5 6 7 a b a Alternate interior angles and 0 b Alternate exterior angles and 20 20 and 20 c Corresponding angles X

ans wants to measure the height of a tree He sights the top of the tree using a mirror that is lying flat on the ground The mirror is 37 ft from the tree and ans is standing 10 6 ft from the mirror as shown in the figure His eyes are 5 ft above the ground How tall is the tree Round your answer to the nearest foot The figure is not drawn to scale 5 ft 10 6 ft 37 ft 0 ft X

A woman wants to measure the height of a nearby building She places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building The total length of the building s shadow is 166 ft and the pole casts a shadow that is 5 5 ft long How tall is the building Round your answer to the nearest foot The figure is not drawn to scale Shadow of pole Pole Shadow of building Sun Building ft

59 6 A positive angle less than 2 that is coterminal with 59 6 is

19T 4 A positive angle less than 2x that is coterminal with 19T is

Which of the following graphs is the correct plot of y 3 cos x TT 3 2 4 2 2 2 5 1 J 2 O 2 3 3 4 15 5 2 in O 6 C 4 2 1 3 1 2 3 4 40 5 6

Choose the correct graph below Draw the angle in standard position State the quadrant in which the angle lies Work the exercise without converting to degrees 11T 6 O A x The angle is in quadrant OB point s possible O C Submit test O D

Which of the following graphs is the correct plot of Y 3 2 5 54 3 3 2 1 st 1 2 C 3 4 5 4 15 6 4 3 d 1 a st 1 2 3 4 5 4 sin x 6 5 4 3 2 1 2 3 4 D st 1 2 O 4 5 6

1 Solve for the variable a b k given sink cos 7k 30 given 1 cot 98 15 1 tan 18 36

tan 18 tan 18x Simplify your answer including any radicals Use integers or fractions for any numbers in the expre

9t sin COS 4 9 sin COS 4 2 3 2 3 COS sin 8 9x 2 4 3 cos 9T sin 2 3 0

sin 0 7 25 0 in Quadrant II cos 0 Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in

Use the triangles given on the right to evaluate the expression given below If necessary express the value without a square root in the denominator by rationalizing the denominator 2 tan cos tan 3 J T 6 4 C 4 45 V A 1 45 1 60 2 1 30 M V3 T 2 tan cos tan 3 6 Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Rationalize all denominators

T Use the unit circle to find the value of tan and even or odd trigonometric 3 functions to find the value of tan 1 0 Ay 0 1 0 1 3 1 0 41 13 Q G Select the correct choice below and fill in any answer boxes within your choice A T 3 Type an exact answer using radicals as needed Simplify your answer Rationalize the denominator tan OB The expression is undefined

15x Choose the figure that shows an angle of 4 Choose the correct answer below O A O radians in standard position then state in which quadrant the angle lies OB G O C G O D

For 0 225 find the three OG trig function values

onvert 3 radians to degrees Approximate to the nearest thousandth

2 Complete the proof of the sine sum identity in the space below sin cos 90 B Letting B A B Q C sin A B cos 90 A B b d 06 8 proved previously along with cos sin 90 cos 90 A B cos 90 A cos B sin 90 A sin B

convert 340 to radians to degrees Convert 23 to 18 Crive a exact answer

Use a double angle formula to rewrite the expression 4 sin x cos x 5

Find x correct to 2 decimal places 185 55 17 X 42

If 0 12 then find exact 4 values for these Sec 0 sc 0 tan 0 cot 0

B C 1 Ad b Suppose a 7 b 11 Find exact value or give at least two decimal places Sin A Cos A tan A a 7 sec A csc A cot A

LAT If 0 47 then 3 sin 0 Cos o Give exact values

Convert the angle in radians to degrees 3x 3x 4 radians radians

If 0 5TT 2 6 sin 0 cos 0 then Give exact values No decimals allowed 2 Example Enter sqrt 2 2 for 2 sqrt 2 2 will work but sqrt2 2 will not With functions like sqrt be sure to use function notation pare

Find the exact value tan 2190 cot 2190

If sin 0 cos 0 1 and is in the 2nd quadrant find cos 0 6

6 5 4 b O C 6 d 5 14 13 2 The plot above is created with the parametric equations x t a cos bt ly t c sin dt To acheive this graph a 2 3 1 2 3 4 of

Find R and 8 given the components R 4 788 and Ry 8 008 R 9 330 Round to the nearest thousandth as needed 0 Type your answer in degrees Use angle measures greater than or equal to 0 and less than 360 Round to the nearest tenth

With the given set of components find R and 0 R 713 R 216 R Round to the nearest integer as m

This is a student s attempt to solve for c I need to explain what the student did right and what they did wrong I have determined that they attempted to use the Bisector Theorem but I am having a hard time explaining it Can you please give me some tips Thank you Student Solution 2 3 10 cos 60 2 1 2 7 2 20 5 C E 2

For each of the following angles find the radian measure of the angle with the given degree measure you can enter as pi in your answers 250 290 170 80 260

a B Find a 11 6 Note Triangle may not be drawn to scale Suppose c 12 and A 75 degrees b 2 5 B 15 b IL C A X 00 00 degrees

8 In AABC points X Y and Z are on sides CB AC and AB respectively so that cevians AX BY and CZ are concurrent at P Prove that sin ZABY sin ZBCZ sin ZCAX sin ZACZ sin ZBAX sin ZCBY

If the perimeter of a rectangle is 70 feet and its area is 196 square feet find the dimensions of the rectangle Let length be the longer side of the rectangle Length type your answer feet Width tyre vale Sama

The graph of y sin is obtained by shifting the graph of y sinx unit s to the right

Use the formula to find the value of the missing variable t t 0 4 0 5 radians 7 11 radian per minute min Simplify your answer Type an integer or a fraction

4 y 2cot 3x 5 2 amplitude period phase shift vertical shift

Match the given function to one of the graphs y 4 cos 2x Choose the correct graph below OA Q B Q Q O C O D

Sketch the graph of the given function Check the graph using a graphing calculator 6 y sinx Choose the correct graph below OA Q Q OD 2 R

1 For 9 points sketch f x secx over the half open interval 7 27 377 2 TC 7 2 2 1 7 2 T 37 2 2 57 2

Find the exact function value tan tan 3x 4 3x 4

Solve the right triangle Round your answers to the nearest tenth 0 0

oose the correct answer below A Pr B Pr n r n D n n r n C nPr r n r

Explain why the triangles are similar 15 The two triangles have two pairs of sides in the same ratio and the angles are also equal The sum of the three angles in each triangle is 180 Both triangles are right The vertical angles in the triangle are equal in measure