Ariel G.

asked • 04/11/21

trig equation help! please explain step by step

Solve the following, where 0° < 𝜃 < 360°.

Find 𝜃 where tan𝜃 = tan265° and 𝜃 ≠ 265°.


What do I do after I found the reference angle of -95°?

please explain this whole question!

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Philip P. answered • 04/11/21

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All trig functions are periodic, meaning they repeat. The tangent function repeats every 180°. So for a given value of θ, you'll get the same value of the tangent by adding or subtracting a multiple of 180° to θ; that is° θ ± n·180° where n = 1, 2, 3, ... So:


tan(265°) = tan(265° - 180°) = tan(265° + 180°), etc


But you need the one that lies between 0 and 360°.

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Ariel G.

tysm! can you tell me the rule for cos and sin as well? like now I know that tan is either - or + 180, are sin and cos like that too? or are there a different method?
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04/11/21

Philip P.

Sine and cosine are a bit more complicated. You can add multiples of a period, just like we did for the tangent. The period for sine and cosine is 360 degrees, rather than 180 degrees as it is for the tangent. But within a given 360 degree period, there are usually two angles that have the same sine or cosine value. To find the second angle, you need to find an angle with the same reference angle in a quadrant with the same sign. So 265 degrees has a reference angle of 85 degrees and sin(265) is negative, There are three other angles with the same reference angle: 85, 95, and 275 degrees. 85 degrees is in quadrant I where the sine is positive. 95 degrees is in quadrant II where the sine function is also positive. 275 degrees is in quadrant IV where the sine is negative, so sin(265) = sin(275).
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04/11/21

Raymond B. answered • 04/13/21

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theta = 85 degrees


tan85 = tan265. In 1st & 3rd quadrants tangents are always >0


tan85= about 11.43

cot85 = about 0.0875

sin85= about 0.996

cos85 = about 0.087

csc85 = 1/sin85 = about 1.004

sec85 = 1/cos85 = about 11.49


just use a calculator with trig functions. plug in 85, then sin, cos, tan

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