Unit 5 Review

Name the Identity

100

csc(x) = 1/sin(x)

reciprocal identity

200

tan(x) = sin(x)/cos(x)

Quotient Identity

300

cos(a)cos(b)-sin(a)sin(b)

addition identity for cosine (cos(a+b))

400

This is the double angle identity for sine

sin(2a) = 2sin(a)cos(a)

Law of Sines and Cosines

100

This is the equation for the Law of Sine

sin(A)/a = sin(B)/b = sin(C)/c

200

Name all 3 equations for Law of Cosines

a² = b²+c² - 2bc(cos(A)),

b² = a²+c² - 2ac(cos(B)),

c² = a²+b² - 2ab(cos(C))

300

c = 21.5, a = 25.4, B = 76.2°

Which Law do you need to use to find b?

Law of Cosines

400

If you are given two angles and 1 side of a triangle, which Law would you need to use to solve for the missing values of the triangle?

Law of Sines

Inverse Trig

100

If sin(25°) = 0.42, what does sin^-1(0.42) = ?

25°

200

If the angle x is between 0 and 2π, what are ALL of the solutions of sin^-1(√3/2) = x?

x = (π/3) and (2π/3)

300

a = 37cm, c = 29cm, C = 50°

What is the measure of angle A?

78°

400

How do we find ALL of the solutions to tan^-1(1) without using a calculator? Name all the steps you need to take. (Use Radian measures)

1. tan = sin/cos

2. tan = 1 in Q1 and Q3

3. π/4 + (2π)n and 5π/4 + (2π)n

Trig Misc.

100

The amount of time it takes for a trig function to complete one full cycle

period

200

In the equation 5cos(π(t-3))+10, what does the value 5 represent?

amplitude

300

What is the alternate area formula for triangles?

A = 1/2*sin(C)*a*b

A = 1/2*sin(B)*a*c

A = 1/2*sin(A)*b*c

400

If we know the position on the unit circle at an angle θ, how do we find the position at the angle 2θ?

We know cos(θ) and sin(θ) so we use the double angle identities to find cos(2θ) and sin(2θ).