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Pre-calculus
Unit 1 Posttest Review
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SHOW WORK. Circle your final answer.
1
1) Find the exact value of cos (x – y) if sin 𝑥 = − 2 and cos 𝑦 =
√3
.
2
X is in the 4th quadrant, and y is in the 1st
quadrant.
2) Is this function even or odd: 𝑦 =
sin 𝑥
𝑥
3) Image you are standing 20 feet away from a tree that is 80 feet tall. What is the angle (in degrees) your feet
makes with the tree?
4) Triangle ABC is a right triangle in the coordinate plane with A being at (0,0) and B at (9,12). Find the tan <BAC
and cos <BAC.
5) A ladder leaning against a wall makes an angle of 45º with the ground. If the length of the ladder is 20 feet, find
the approximate distance of the foot of the ladder from the wall.
6) Solve: 2𝑠𝑖𝑛2 𝑥 − 𝑠𝑖𝑛𝑥 − 1 from 0° ≤ 𝑥 ≤ 90°
7) Solve: 4𝑐𝑜𝑠 2 𝑥 − 1 = 0 from 0° ≤ 𝑥 ≤ 360°
Pre-calculus
Unit 1 Posttest Review
8) Find the exact value of sin 70°.
9) If sin -200° = .34 and sec -200° = -1.06, find the csc and cos of -200°.
10) Draw an example of an odd function.
11) What is the period of 𝑦 = 6𝑠𝑖𝑛3𝑥?
1
12) What is the value of the arccos (− 2)?
𝜋
13) What trigonometric function has the same value as 𝑠𝑖𝑛 11?
14) Simplify
cos 2𝑥+cos 4𝑥
sin 2𝑥
.
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Pre-calculus
Unit 1 Posttest Review
15) What is the cofunction identity for sin Ɵ?
16) Write the expression that completes the identity: cos µ cos α =
17) Rewrite the expression as a double-angle identity: 𝑐𝑜𝑠 2 𝜃 − 𝑠𝑖𝑛2 𝜃
18) Rewrite the expression as a half-angle identity: sin 165®
19) In a right triangle, if < 𝜃 = 30° and the hypotenuse is 4, what is the exact length of the long leg?
20) What is the right triangle definition of secant and cosecant?
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