Pre-Calc UE5 Review

Solve

100

Solve cos(x)+sqrt(3)=-cos(x)

5pi/6, 7pi/6

200

How many solutions exist for cos(x)=1/2 on the interval (0, pi)?

1

300

Solve sin(2x) + cos(x) = 0

7pi/6, 11pi/6

400

Solve sqrt(2)+sin(x) = -sin(x)

5pi/4, 7pi/4

500

Solve cos(2x)+cos(x)=0

pi/3

Simplify

100

Simplify sin(x)sec(x)

tan(x)

200

Simplify csc²(x)/sec²(x)

cot²x

300

Simplify sec(x)-tan(x)sin(x)

cos(x)

400

Simplify (1-cos²x)/sin²x

1

500

Simplify sin²(x)-sin²(x)sec²(x)

cot²x

Sum/ Difference

100

Find cos(105)

(-sqrt(6) + sqrt(2))/4

200

Find sin(195)

(sqrt(2) - sqrt(6))/4

300

Find sin(225)

-sqrt(2)/2

400

Find cos(255)

(-sqrt(6) + sqrt(2))/4

500

Find cos(285)

(sqrt(6) - sqrt(2))/4

Double and Half Angle Formulas

100

If cos(A)=24/25 and sin(A)=7/25, then what is sin2A?

336/625

200

If cos(A)=8/17 and sin(A)=15/17, then what is sin2A?

240/289

300

If cos(A)=6/10 and sin(A)=8/10, then what is sin2A?

96/100 or 24/25

400

You have an 8-15-17 triangle. Determine sin(x/2) if cos(x)=8/17.

0.51

500

You have an 9-40-41 triangle. Determine cos(x/2) if cos(x)=9/41.

0.78

Law of Sines/ Cosines

100

m∠A = 70°, c = 26, a = 25. Solve for angle C.

77.8

200

m∠B = 45°, a = 28, b = 27. Solve for angle A.

47.2

300

Angle A=64°, Angle B=98°, a= 29mi Find b

32 mi

400

In ∆ABC, a = 14 cm, b = 9 cm, c = 6 cm. Find angle A.

137

500

n ∆XYZ, m∠X = 138°, y = 15 in, z = 25 in. Find angle Y.

15.5