Trigonometry Questions and Answers

Graph the function and y = cos x in the same rectangular system for 0 ≤ x ≤ 2π y = 3 cos x

cos θ =2/3 ,tan θ<0 find sin θ -3/2 -√5 -√5/3 -√5/2

cos x + sinx/cosx - sinx-cos/sinx sec x csc X 2 + sec x csc X 1 - sec x csc X 2 - sec x csc X

Complete the identity. sin^2 x + tan^2x + cos^2x = ? sec² x tan² x cot³x sin x

Solve the equation on the interval [0, 2π). cos^ 2 x + 2 cos x + 1 = 0 π /2 ,3π/7 π π/4,7π/4 2π

From the professor's perspective, explain the pros and cons of using the method below in finding trigonometric values of special angles. Then present an example to illustrate the process. (a) reference angle method (b) unit circle method

Solve for the exact solutions in the interval [0, 2π) . Separate solutions with a comma. If the equation has no solutions, respond with DNE. sin(4x) = 1/ 2

Find the least positive value of θ tan(7θ-4°) =1/cot(6θ+4°)

Find the least positive value of θ cos(2θ-8°)sec (3θ- 18°) = 1

Find a value of a in [0°, 90°] that satisfies the given statement. csc a= 1.2763014

Find the least positive value of θ sec(2θ+4°)cos(3θ-2°) = 1 θ=

Given the equation y=4 csc(3π/4 x + 21π/x) The period is: The horizontal shift is:__units to the Select an answer

If f(x) = 3 cos(x), 0≤x≤3π/4 Find the width of each subinterval. Find the left endpoints of the subintervals where x₁ < x2 <......... < X6. x1 x2 x3 X4 X5 X6 evaluate the left Riemann sum with n = 6, taking the sample points to be left endpoints. Evaluate the Reimann sum. (Round your answer to six decimal places.)

Evaluate sin (cos-¹(x/8)). √64-x²/8 8/√64-x^2 √x²-64/8 8/√x²-64 None of These

Find linear approximation of the given quantity: sin 122° Round your answer to 4 d.p.

Graph on period of y = -tan(-1/4x+π/8) centered at the phase shift, including all roots and asymptotes -The standard form y = -tan(-1/4(x-(-π/2))

Given that cos A =-4/5 with angle A in quadrant II and sin B = -24 /25 with angle B in quadrant III. Find cos(A + B) none of these 3/5 4/5 -4/5 -3/5

Choose 1 of the 2 trigonometric equations below to solve for x. Express your answer(s) in the interval [0, 2x) a. cos(2x)-cosx=0 b. 4tan^2 x + 4tanx=0

Prove the following identities. Show all of your work for full marks! Do not skip steps! a) sin²xcos²x+cos4x = (1-sinx)(1+ sin x) b) sinxtanx+ sinx tanx = 1 cosx

The distance from the Sun to Earth is approximately 149600000 km. Assuming Earth has a circular* orbit around the Sun, find the distance Earth travels in orbiting the Sun through an angle of 3.64 radians. *Be it noted that the planets orbiting the Sun actually have elliptical orbits, not circular. 544650100 km 544664000 km 544688575 km 544544000 km None of the above

Find the quotient and write it in rectangular form using exact values. 8( cos 120° + i sin 120°) 2 (cos 150° + i sin 150°)

Airports A and B are 444 km apart, on an east-west line. Jim flies in a northeast direction from A to airport C. From C he flies 347 km on a bearing of 125°50' to B. How far is C from A?

A triangular swimming pool measures 46 ft on one side and 32.8 ft on another side. The two sides form an angle that measures 41.3°. How long is the third side?

Write the complex number in rectangular form. 7 cis 315° The complex number is

Determine the number of triangles ABC possible with the given parts. A 39.8° a 3.5 c= 8.4 How many possible solutions does this triangle have?

A triangular swimming pool measures 42 ft on one side and 32.8 ft on another side. The two sides form an angle that measures 40.6°. How long is the third side?

Rewrite cos (x + 2π/3) in terms of sin(x) and cos(x).

Simplify sin(π – u) to a single trig function using a sum or difference of angles identity.

Without using a calculator, find the value of sin² (5°) + cos² (5°) - sin(60°)/cos(30°)

Solve sin(2x)cos(7x) – cos(2x)sin(7x)=-0.8 for the smallest positive solution.

Solve sin(4x) cos(9x) - cos(4x) sin(9x) = - 0.1 for the smallest positive solution

Consider the following parametric equations: x = sin(θ) + 2 and y= 2sin(θ)-2 Step 2 of 2: Determine the domain and range of the equation obtained by eliminating the parameter. Please write your answer in interval notation.

Simplify sin(t)sec(t) to a single trig function or constant with no fractions.

Simplify tan(t) / sec(t) to a single trig function with no fractions.

Simplify sin² (t)/1-sin² (t) to an expression involving a single trig function with no fractions. If needed, enter squared trigonometric expressions using the following notation. Example: Enter sin² (t) as (sin(t))².

Determine the value of sin² x + cos²x for x = 60 degrees.

Fill in the blanks: 1. If tan x = 0.5 then tan( − x) = 2. If sin x = 0.4 then sin( -x) c= 3. If cos x = 0.5 then cos( x ) = 4. If tan x = -3 then tan(π + x) =

Simplify 1 + cot(t)/1+tan(t) to a single trig function with no fractions.

Find the values of the trigonometric functions of t from the given information. sin(t) = 4/5, terminal point of t is in Quadrant IV cos(t) = tan(t) = csc(t) = sec(t) cot(t):

Verify the identity. (cscx – cotx)^2 = 1- cos x / 1 + cos x

A student solved this question: Find the value(s) of x within 0 ≤ x ≤ 2π for the following expression sin² (2x) + = = 2sin(x) cos(x). Did they make any mistakes in their work below? If yes, show where the mistakes are by explaining what they did wrong. Then fix the problem to get the correct answer based on the question.

Use the sum or difference formula for tangent to find the exact value for tan(-75°) tan(-75°)

The point of concurrency of the perpendicular bisectors of a triangle is called the centroid. incenter. orthocenter. circumcenter.

Find the exact value of sin(75°).

Determine the quadrant when the terminal side of the angle lies according to the following conditions: sin (t) > 0, tan (t) <0. Quadrant I Quadrant III Quadrant IV Quadrant II

Find the value of the trigonometric function sin (t) if sect=-4/3 and the terminal side of angle t lies in quadrant II. sin (t) = 3/4 sin (t) =√5/4 sin (t) = 5/4 sin (t) = √7/4

For 0 < θ<π/2, find the values of the trigonometric functions based on the given one (give your answers with THREE DECIMAL PLACES or as expressions, e.g. you can enter 3/5). If cos(θ) = 5/11 then sin(θ) = sec(θ) = csc (θ) = tan(θ) = cot(θ) =

Find a positive angle less than one revolution around the unit circle that is co-terminal with the given angle: 52π/5 8π/5 12π/5 5π/2 2π/5

In which quadrant is the following true? cscx<0 and secx>0 Quadrant IV Quadrant III Quadrant I Quadrant II

For an angle A in standard position, if sinA=cosA then the terminal arm of the angle lies in quadrants II or IV. True False