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Dana Herzog

Feb 20, 2025

How do you find the exact trigonometric ratios for the angle 3pi/4?

I took precalculus 2 years ago and i don't remember where to start with this type of problem. Can someone please show me what i need to do to find the lengths of the triangle and then calculate the ratios to answer the problem? Please make sure your answer is thorough as i am a bit rusty with this stuff.
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With every angle there is associated a reference angle, which is the positive acute angle that the terminal side of the given angle makes with the (positive or negative) x-axis. An angle and its reference angle have the same value for their trig functions, except possibly for sign.3π/4 is in the second quadrant, so its cosine is negative and its sine is positive. From these you can determine the sign of the other four trig functions.The reference angle for 3π/4 is π/4. This is an angle for which you are expected to know at least the sine and cosine: sin(π/4) = cos(π/4) = √2 / 2. Therefore, sin(3π/4) = √2 / 2cos(3π/4) = -√2 / 2tan(3π/4) = sin(3π/4)/cos(3π/4) = -1csc(3π/4) = 1/sin(3π/4) = √2sec(3π/4) = 1/cos(3π/4) = -√2 cot(3π/4) = 1/tan(3π/4) = -1... Show More
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