Trigonometric Identities Unit Test

Use a half-angle identity to find the exact solution of cos 3pi/8

A

Use a half-angle identity to find the exact value of sin75

A

Which is the standard form of the equation of p=21, phi= 7pi/6?

A

Use the given information to determine the exact trigonometric value sin(theta)= -1/5, pi < theta < 3pi/2, cos (theta)

A - 2 sqrt6 /5

What basic trigonometric identity would you use to verify that sinx cox tanx = 1-cos^2 X?

A tanx= sinx/cosx

Which sum or difference identity would you use to verify that sin(90+theta)= cos(theta)

B

Assume that 0 < x < pi/2 and 0 < y < pi/2. Find the exact value of tan (x-y) if sinx= 8/17 and cosy= 3/5

B -36/77

Express cos 7pi/3 as a trigonometric function of an angle in Quadrant 1

B cos pi/3

What basic trigonometric identity would you use to verify that cscx secx cotx= csc^2 x

B cotx= cosx/sinx

Write the standard form of an equation with p=3 sqrt2, phi=135

B x-y + 6=0

Simplify the expression secx/tanx

B cscx

If a and b are the measures of two first quadrant angles and sina=4/9 and sinb=2/5 find sin(a+b)

C

Write the equation x=5y-2=0 in normal form. Then, find the length of the normal and the angle it makes with the positive x-axis

C

Simplify the expression cosx cscx tanx

C 1

Use a half-angle identity to find the exact value of tan 5pi/12

C 2 + sqrt3

Find the exact value of sin165

C sqrt6 + sqrt2 /4

Use a half-angle identity to find the exact value of tan22.5

C sqrt2 - 1

What is the standard form of the equation of a line for which the length of the normal segment to the origin is 8 and the normal makes an angle of 120

D

Given tan(theta)= 4/3 and pi < theta < 3pi/2; find cos 2(theta)

D -7/25

Express 13pi/6 as a function of an angle in Quadrant 1

D pi/6

Which trigonometric function is equivalent to sec(-270)?

D sec(90)

Given that 1+ cosx/sinx + sinx/1+cosx =4, find a numerical value of one trigonometric function of x

D sinx= 1/2

Find csc x if sin c + cot x cos x= sqrt3

D sqrt3

Consider a line l with postive-x and y-intercepts. Suppose l makes an angle of theta with the positive x-axis. What is the slope of l in terms of theta?

D tan(theta)

Ancient slingshots were made form straps of leather that cradled a rock until it was released. One would spin the slingshot in a circle, and the initial path of the released rock would be a straight line tangent to the circle at the point of release.The rock will travel the greatest distance if it is release when the angle between the normal to the path and the horizontal is -45. The center of the circular path is the origin and the radius of the circle measure 1.25 feet.Write and equation of the initial path of the rock in standard form.

maybe C NOT B