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Trigonometry Course for Cambridge IGCSE Mathematics (0580) Extended 

 ( A Comprehensive Self-Study Course for UK and International (IGCSE) Mathematics Learners Globally)

Q1 Find all the solutions in the interval 0≤θ≤360 for sin x =1/2, without drawing the graph.

Solution: sin 30°=1/2,

X=30°

Sine is positive in second quadrant so other solution must be 180°-θ

Second answer = 180-x=150°

Two solutions are 30°, 150°

Q2 Solve 4sin x-3=0 for 0°≤x≤360°

Sin x =3/4=0.75

x=sin⁻¹0.75=48.6°

180°-x=180°-48.6°=131.4°

Q3 Solve tan x= 1 for 0°≤x≤360° (can be asked without calculator)

x=tan⁻¹ 1=45°

Tan is positive in first and third quadrant, so second solution must be in third quadrant.

180°+45°=225°

Q4 Solve sin x=0.3 for 0°≤x≤360°

x=sin⁻¹0.3=17.5°

180°-x=180°-17.5°=162.5°

Q5 Solve sin x= 1/√2 for 0°≤x≤360° (can be asked without calculator)

x=sin⁻¹ (1/√2)=45°

180°-45°=135°

Q6 Solve cos x= 0.5 for 0°≤x≤360° (can be asked without calculator)

x=cos⁻¹ (0.5)=60°

360°-60=360°-60°=330°

Q7 Solve cos x= 0.9 for 0°≤x≤360°

x=cos⁻¹ (0.9) = 25.8°

360°-25.8°=334.2°

Q8 Solve tan x= 3 for 0°≤x≤360°

x=tan⁻¹ 3=71.6°

Tan is positive in first and third quadrant, so second solution must be in third quadrant.

180°+71.6°=251.6°

Q9 Solve √2sin x+1= 0 for 0°≤x≤360°

Answer 225°, 315°

Q10 Solve tan x+√3= 0 for 0°≤x≤360°

Answer 120°, 300°

Explore the Trigonometry Complete Preparation course for free video Lectures

Trigonometry Course for Cambridge IGCSE Mathematics (0580) Extended 

 ( A Comprehensive Self-Study Course for UK and International (IGCSE) Mathematics Learners Globally)