📝 Chapter 4: Trigonometry

Convert: a) 150° to radians b) 7π/4 to degrees c) Find arc length: r=8cm, θ=3π/4

Evaluate exactly (no calculator): a) sin(2π/3) b) cos(5π/6) c) tan(4π/3) d) csc(π/4)

Use compound angle formulas to find the exact value of: a) cos(π/12) b) sin(7π/12)

Simplify using identities: a) (1-cos²x)/sin x b) sin²x + sin²x·tan²x

Verify the identity: sec²x - 1 = tan²x, starting from the Pythagorean identity.

Prove: (sinx + cosx)² + (sinx - cosx)² = 2

Prove: (1 + tanx)/(1 - tanx) = (cosx + sinx)/(cosx - sinx)

If sin(a) = 3/5 (a in Q1) and cos(b) = -12/13 (b in Q2), find the exact value of sin(a+b).

A student claims cos(A+B) = cosA + cosB. Find specific values of A and B that disprove this. Then state the correct formula.

Explain why sin(π/6) = cos(π/3). Use a diagram, the unit circle, and the concept of co-function identities.

Write a step-by-step method for proving trigonometric identities. Include at least 3 strategies (e.g., convert to sin/cos, factor, use Pythagorean identities). Demonstrate with one example.

Create a study summary of the compound angle formulas (sin(A±B), cos(A±B), tan(A±B)) including the double angle formulas. Organize clearly with examples.

Explain, using diagrams, why radian measure makes the formula s = rθ so simple compared to using degrees. What would the formula look like with degrees?

A Ferris wheel has radius 15m and its center is 18m above the ground. If it takes 2 minutes for one revolution, find the rider's height after 20 seconds using trigonometry with radian measure.

Two boats leave a dock. Boat A travels at bearing 060° for 10km. Boat B travels at bearing 150° for 8km. Find the distance between the two boats using the cosine law with radian measure.

An electrical signal is modeled by V(t) = sin(t) + sin(t + π/3). Use the compound angle formula to express V(t) as a single sinusoidal function.

A surveyor needs to find the height of a building. From point A, the angle of elevation is π/6. After walking 50m closer (point B), the angle of elevation is π/4. Find the height of the building.