Find the exact value of tan((cos^-1)(12/13))

QUESTION POSTED AT 16/04/2020 - 06:33 PM

Answered by admin AT 16/04/2020 - 06:33 PM

Let x=\cos^{-1}\dfrac{12}{13}, so that \cos x=\dfrac{12}{13}.

Recall that

\cos^2x+\sin^2x=1\implies\sin x=\dfrac5{13}

where we take the positive root because \cos\theta is only invertible if 0\le\theta<\pi, and \cos\theta>0 only if 0\le\theta<\dfrac\pi2, which means \sin\theta>0.


\tan\left(\cos^{-1}\dfrac{12}{13}\right)=\tan x=\dfrac{\sin x}{\cos x}=\dfrac{\frac5{13}}{\frac{12}{13}}=\dfrac5{12}
Post your answer

Related questions

Find the six arithmetic means between 1 and 29.

QUESTION POSTED AT 02/06/2020 - 01:36 AM

Three-sevenths of a number is 21. Find the number

QUESTION POSTED AT 01/06/2020 - 04:54 PM

The lengths of three sides of a quadrilateral are shown below: Side 1: 3y2 + 2y − 6 Side 2: 3y − 7 + 4y2 Side 3: −8 + 5y2 + 4y The perimeter of the quadrilateral is 4y3 + 18y2 + 16y − 26. Part A: What is the total length of sides 1, 2, and 3 of the quadrilateral? (4 points) Part B: What is the length of the fourth side of the quadrilateral? (4 points) Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points) QUESTION 2: A rectangle has sides measuring (4x + 5) units and (3x + 10) units. Part A: What is the expression that represents the area of the rectangle? Show your work to receive full credit. (4 points) Part B: What are the degree and classification of the expression obtained in Part A? (3 points) Part C: How does Part A demonstrate the closure property for polynomials? (3 points) QUESTION 3: A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 5t, where t represents time in minutes and p represents how far the paint is spreading. The flowing paint is creating a circular pattern on the tile. The area of the pattern can be expressed as A(p) = πp2. Part A: Find the area of the circle of spilled paint as a function of time, or A[p(t)]. Show your work. (6 points) Part B: How large is the area of spilled paint after 2 minutes? You may use 3.14 to approximate π in this problem. (4 points)

QUESTION POSTED AT 01/06/2020 - 04:46 PM