Problems:
Solving Trigonometry functions
1. Find the exact value of the sine, cosine, and tangent of the angle. 11pie/12
2. Find all solutions of the equation in the interval [0, 2pie).
Sin(x-5pie/6)-sin(x+ 5pie/6) =1
3. Find the exact value of sin2x using the double angle formula. Please help explain the use of the double angle formula.
Sin x=1/7, 0
4. Given cos theta = 4/9, where 3pie/2
5. Express 2sin3xcos6x as a sum containing only sines or cosines.
6. Express cos7x-cos5x as a product containing only sines and/or cosines.
7. Evaluate the expressions without the aid of a calculator.
a. Arctan(- sqrt3/3)
b. Arcsin(-1/2)
8. Use inverse functions to evaluate the expressions,
a. cos(arcsin(sqrt5/5))
b. cos(arctan(sqrt2/x))
9. Identify the x-values that are solutions of the equations.
a. 8cos x-4 = 0
b. 18cot^2 x-18 = 0
10. A large pole is 175 feet tall. On a particular day at noon it casts a 198-foot shadow. What is the sun's angle of elevation?