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Trigonometry - Solving equations.
Test Yourself 1.


 

The questions below focus on the formats:
1. Trig ratio and a constant
2. Squared trig ratio and a constant.
3. Sin and cos terms but no constant.
4. Trig ratios in a quadratic format.
5. Using angles of any magnitude.
6. Number of solutions.

 

1. Trig ratio and a constant.    
     
   
   
     
2. Squared trig ratio and a constant.    
     
     
3. Sin and cos terms but no constant.    
     
     
     
4. Trig ratios in a quadratic format.

Find the exact solutions for θ given the equation

2sin2 θ - sin θ -1 = 0

 

Solve for θ:

2cos2θ + 3 sinθ cosθ + sin2θ = 0

(0 ≤ θ ≤ 360°).
 

(i) Show that

(cosec2 A - 1)sin2 A = cos2 A

(ii) Hence or otherwise solve

(cosec2A - 1)sin2A = 0.75

for -π ≤ A ≤ π

  
     

5. Using angles of any magnitude.

0 ≤ θ ≤ 90°

  
     
6. Number of solutions. How many solutions are there for the equation 0 ≤ x ≤ 2π.

(2cos 2x - 1)(sin2 x + 1) = 0

How many solutions are there between 0 and 2π for the equation

(sin x - 1)(tan x + 2) = 0