Find the reference angle for the angle -frac{25 pi}{4}

Question

Accepted Answer

Step:1 ：Given the angle (-frac{25 pi}{4})Step:2 ：We first find the equivalent positive angle that lies between 0 and (2pi) by adding multiples of (2pi) to the given angle until we get a positive angle in this range.Step:3 ：The equivalent positive angle is (frac{11 pi}{4})Step:4 ：We then find the reference angle by subtracting the largest multiple of (frac{pi}{2}) that is less than or equal to the equivalent positive angle.Step:5 ：The largest multiple of (frac{pi}{2}) that is less than or equal to (frac{11 pi}{4}) is (frac{10 pi}{4})Step:6 ：So, the reference angle is (frac{11 pi}{4} - frac{10 pi}{4} = frac{pi}{4})Step:7 ：Final Answer: (boxed{frac{pi}{4}})

Answer

Step: 1 ：Given the angle (-frac{25 pi}{4})Step: 2 ：We first find the equivalent positive angle that lies between 0 and (2pi) by adding multiples of (2pi) to the given angle until we get a positive angle in this range.Step: 3 ：The equivalent positive angle is (frac{11 pi}{4})Step: 4 ：We then find the reference angle by subtracting the largest multiple of (frac{pi}{2}) that is less than or equal to the equivalent positive angle.Step: 5 ：The largest multiple of (frac{pi}{2}) that is less than or equal to (frac{11 pi}{4}) is (frac{10 pi}{4})Step: 6 ：So, the reference angle is (frac{11 pi}{4} - frac{10 pi}{4} = frac{pi}{4})Step: 7 ：Final Answer: (boxed{frac{pi}{4}})

Find the reference angle for the angle $- \frac{25 π}{4}$

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Find the reference angle for the angle −25π4

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Popular Problems

Find the reference angle for the angle $- \frac{25 π}{4}$