1. If angle θ is in the first quadrant and cos(θ) = 3/5 then what is sin(θ)?
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Correct answer is option - 3
Explanation: If cos(θ) = 3/5, then sin(θ) = √(1 – cos^{2}(θ)).
This gives: sin(θ) = √(1 – (3/5)^{2}) -> √(1 – 9/25) = √[(25 – 9)/25].
This gives: sin(θ) = √(16/25) -> sin(θ) = 4/5.
In the first quadrant, all trigonometric functions are positive!
2. What is the value of cos(θ) if θ = 480°?
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Correct answer is option - 1
Explanation:The given angle 480° can be written as 480° = 360° + 120°.
So, cos(480°) = cos(360° + 120°) which is equal to cos(120°).
cos(120°) can be written as cos(90° + 30°) = - sin(30°) = -1/2.
(Since this angle falls in the second quadrant and ‘cosine’ is negative in that quadrant. Hence we get a negative value).
3. What is the value of 330° in radian measure?
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Correct answer is option - 4
Explanation:330° can be written in radian measure as 330° * (π/180°).
This can be simplified to 33π/18 which can be further simplified to 11π/6.
4. The trigonometric expression (1 + cosθ)(1 – cosθ) can be simplified to?
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Correct answer is option - 2
Explanation: The trigonometric expression, (1 + cosθ)(1 – cosθ) is in the form of (a + b)(a – b) and it is equal to a^{2} – b^{2}.
So, (1 + cosθ)(1 – cosθ) = 1 – cos^{2}θ.
According to the trigonometric identity, 1 – cos^{2}θ = sin^{2}θ.
5. The expression, tan (45° + x) can be expanded as?
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Correct answer is option - 2
Explanation:The sum formula for tan (A + B) = (tan A + tan B)/ (1 – tan A * tan B).
Applying the above formula, we get: tan (45° + x) = (tan45° + tan x)/ (1 – tan 45° *tan x).
This gives: tan (45° + x) = (1 + tan x)/ (1 – tan x).