NEED HELP!!
Find all numbers t such that
cos^-1 t = sin^-1 t.
To find all numbers t that satisfy the equation cos^-1 t = sin^-1 t, let's use the properties of inverse trigonometric functions.
First, recall that the range of the sine function sin(x) is [-1, 1] and the range of the cosine function cos(x) is also [-1, 1]. Since the inverse trigonometric functions sin^-1 and cos^-1 have the same range, we can narrow down the possible values of t.
Next, use the identity sin^-1 t + cos^-1 t = π/2. Since sin^-1 t = cos^-1 t, we can substitute and write the equation as 2cos^-1 t = π/2.
Now, solve for cos^-1 t by dividing both sides of the equation by 2:
cos^-1 t = π/4.
The value of t that satisfies this equation is cos(π/4), which is equal to √2/2 or approximately 0.7071.
Therefore, the only number t that satisfies the equation cos^-1 t = sin^-1 t is t = √2/2 or approximately 0.7071.