Trigonometry - finding a trig ratio given the value of another.
Test Yourself 1.
| The 3 basic ratios | 1. If sin θ = 3/5 and cos θ < 0, find the value of tan θ if 0° ≤ θ ≤ 360°.
Answer. tan θ = -3/4. |
| 2. If tan α = 5/12 and sin α > 0, find the value of cos α if 0° ≤ θ ≤ 360°.
Answer. cos α = 12/13. |
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| 3. If cos β = 8/17, find the value of sin β if 180° ≤ β ≤ 360°. Answer. sin β = -15/17. |
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| 4. If tan x = 1/3 and cos x < 0, find the value of sin x.
Answer. sin β = -1/√10. |
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| 5. If cos x = -1/3 and sin x < 0, find the value of tan x.
Answer. tan x = √8. |
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| 6. If sin x = -1/2 and tan x < 0, find the value of cos x.
Answer. cos x = √3/2. |
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| 7. If sin x = -1, find the value of cos x.
Answer. cos x = 0. |
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| 8. If cos x = 1/2 and tan x > 0, find the value of tan x.
Answer. sin x = √3/2. |
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| 9. If tan β = -15/8 and 90° ≤ β ≤ 270°, find cos β. Answer. tanβ = -8/17. |
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| 10. If cos θ = 5/7 and 0° < θ < 180°, what are the values for tan θ° and sin θ. Answer. tanθ = -√24 / 5 sinθ = +√24/7. |
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| 11. If cos x = 5/9 and 180° ≤ x ≤ 360° find the value of sin x + tan x - cos x. (to 2 decimal places). Answer.Sum = -2.88. |
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| 12. If tan α = -21/20 and cos α < 0, find sin α.
Answer. sin α = -21/29. |
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| The 3 reciprocal ratios | 13. If sec x = -2 and tan x < 0, find the value of sin x.
Answer. sin x = √3/2. |
| 14. If cot x = -√3 and sin x < 0, find the value of cos x.
Answer. cos x = √3 /2. |
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| 15. If cosec x = -2/√3 and cos x < 0, find the value of cot x.
Answer. cot x = 2/ √5. |
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| 16. If cot θ = 24/7 and sec θ < 0, find the value of cosec θ.
Answer. cosec θ = -25/7. |
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| 17. If cos α = 12/13 and 180° < α < 360°, find the value of cot α. Answer. cot α = -12/5. |
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18. Given cos β = -3/4
Answer.sin β = √7 / 4. cot β = -3 / √7. |
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| 19. If cosec x = -5/2 and cos x > 0, find values for cot x and sec x.
Answer. cot x = -√21/2. sec x = 5/√21. |
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| 20. If sin θ = x and x > 0, find possible values for tan θ and sec θ.
Answer. tan θ = -x/√(1 - x2). sec θ = -1/√(1-x2) |