8/8/2019 Trig Equations - Weekly Review

1/1

IB WEEKLY REVIEW Trigonometric Functions

[N02/520/S(1) #14]

1. Consider the trigonometric equation xx cos1sin2 2 ! .

(a) Write this equation in the form 0)( !xf , where cxbxaxf ! coscos)(2

, and a,b, and c > .

(b) Factorize )(xf .

(c) Solve 0)( !xf for 0 < x < 360.

[M04/521/S(1) #9] and [M04/522/S(1) #9]

2. Solve the equation xx 2sincos2 2 ! for Tee x0 , giving your answer in terms ofT .

[M02/520/S(1) #8]

3. Let xxf 2sin)( ! and )5.0sin()( xxg ! .

(a) Write down(i) the minimum value of the functionf.(ii) the period of the functiong.

(b) Consider the equationf(x) =g(x).

Find the number of solutions to this equation for2

30

Tee x .

[SPEC00/520/S(1) #12]

4. (a) Express xx sincos2 2 in terms of xsin only.

(b) Solve the equation 2sincos2 2 ! xx forx in the interval 0