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Evaluate tan (arccsc-1)

Make sure you show all of the steps needed for evaluating the above composition. No decimals. Give exact values.

arcsec(-1) = π

so, what do you think?

Did you know?

Did you know that the inverse trigonometric functions can be combined to evaluate the value of trigonometric ratios? For example, to find the value of tan (arccsc-1), we can follow these steps: 1. Start with the innermost function, arccsc-1, which represents the inverse cosecant function. This function finds the angle whose cosecant is -1. 2. The cosecant function is the reciprocal of the sine function, so if we find an angle whose sine is -1, we will also find the angle whose cosecant is -1. 3. Since sine is negative in the third and fourth quadrants, we know that the angle we're looking for is in one of these quadrants. 4. To find the angle whose sine is -1, we can take the inverse sine of -1, denoted as sin^-1(-1). This gives us a reference angle of 270 degrees or π radians. However, since we're looking for an angle in the third or fourth quadrant, we need to add 180 degrees or π radians to the reference angle. 5. The resulting angle is therefore 270 degrees + 180 degrees = 450 degrees, or π radians + π radians = 2π radians. 6. Now that we have the angle, we can calculate the tangent of 450 degrees or 2π radians. 7. The tangent function is equal to the sine divided by the cosine, so we evaluate the sine and cosine of 450 degrees or 2π radians. 8. The sine of 450 degrees or 2π radians is equal to 0, and the cosine is equal to -1. 9. Finally, we divide the sine by the cosine to get tan 450 degrees or 2π radians: 0 / -1 = 0. Hence, tan (arccsc-1) is equal to 0.