Download Trig Chapter 6

TRIGNOMETRIC EQUATIONS AND IDENTITIES
DIPLOMA STYLE QUESTIONS
1. Solve for θ, where 0⁰ ≤ θ < 360⁰, in the equation 2cos2θ + cosθ = 0.
2. Determine the general solution of tan2θ – 1 = 0, expressed in radians. (SE)
3. For the equation 2cos2x + sinx – 1 = 0, find all the values of x, where –π ≤ x ≤ π. (SE)
4. Solve for θ, where 180⁰ ≤ θ ≤ 360⁰, given (2 - √3secθ)(secθ + 3) = 0. State answers to the nearest
degree.
5. Find the general solution to the equation sin(2θ) – cosθ = 0. Express the solution in degrees. (SE)
6. Three students were given the identity
𝑠𝑖𝑛2 𝜃−1
𝑐𝑜𝑠𝜃
= -cosθ, where cosθ = 0.
𝜋
3
a) Student A substituted θ = to both sides of the equation and got LS = RS. Student B entered
LS into y1 and RS into y2 and concluded that the graphs are exactly the same. Explain why these
methods are not considered a proof of the identity.
b) Student C correctly completed an algebraic process to show LS = RS. Show a process
Student C might have used.
c) Which non-permissible values of θ should be stated for this identity? (SE)
7. The expression
𝑐𝑜𝑡𝑥+𝑐𝑠𝑐𝑥
,
𝑠𝑒𝑐𝑥+1
A.
sin x
B.
tan x
C.
csc x
D.
cot x
where sec x = -1, is equivalent to (SE)
Use the following information to answer the next question.
Each trigonometric expression below can be simplified to a single numerical value.
1
cot2x – csc2x
2
sec2x – tan2x
3
sin x – 𝑠𝑒𝑐𝑥
4
𝑡𝑎𝑛𝑥
1
cos2x
7
1
+ 7sin2x
8. When the numerical values of the simplified expressions are arranged in ascending order, the
expression numbers are ________, ________,________, and________.
9. What is the exact value of tan 75⁰? (SE)
10. Prove algebraically that
sin  2 x 
2 tan x
 n
, where x  
,n I .

2
2
2
4 2
1  tan x cos x  sin x