Trig Invaders (Solving Trig Equations)
sin(theta) = 1/2, from 0° to 360°
30°, 150°
What is the amplitude of y = 3sin(x)?
3
What is the exact value of cos(60°)?
1/2
What does each letter in CAST stand for?
C = cos+, A = all+, S = sin+, T = tan+ (starting in Quadrant IV)
A 10 m ladder leans against a wall at a 60° angle. How high does it reach?
10 * sin(60°) = 8.66 m
cos(theta) = -1/2, from 0° to 360°
120°, 240°
What is the period of y = cos(2x)?
180°
What is the exact value of tan(45°)?
1
In which quadrants is sine positive?
Quadrants I and II
A ramp rises 5 m and makes a 30° angle. What is the ramp’s length?
5 / sin(30°) = 10 m
tan(theta) = √3, from 0° to 360°
60°, 240°
What is the phase shift of y = sin(x - 90)?
90° right
In a 30°-60°-90° triangle, if the hypotenuse is 8, what is the shorter leg?
4
Simplify: sin(x)/cos(x)
tan(x)
A Ferris wheel has a max height of 25 m and min of 5 m. Write its sine equation.
y = 10sin(x) + 15
2sin(theta) = √2, from 0° to 360°
45°, 135°
Write the equation of a sine wave with amplitude 2, period 360°, and vertical shift +1.
y = 2sin(x) + 1
Use a special triangle to evaluate sin(45°).
√2/2
If y = 6 and r = 10, what is sin(theta)?
0.6
A boat is 100 m from a lighthouse. The angle of elevation is 35°. How tall is it?
100 * tan(35°) ≈ 70.0 m
3cos(theta) + 1 = 0, from 0° to 360°
theta = approx. 109.5°, 250.5°
Sketch one cycle of y = -3cos(x). What are the max, min, and midline?
Max: -3, Min: 3, Midline: 0 (reflection of regular cosine wave)
Given sin(A) = 1/2, what is angle A in a right triangle?
30°
Prove the identity:
(1 - sin²(x)) / cos(x) = cos(x)
Left side:
(1 - sin²(x)) / cos(x)
= cos²(x) / cos(x) [since 1 - sin²(x) = cos²(x)]
= cos(x)
= Right side ✔️
A person sees the top of a building at 50° and the base at 10°, from 60 m away. Find the height.
60 * (tan(50°) - tan(10°)) ≈ 60.9 m