Question Video: Using Inverse Trigonometric Functions to Solve Trigonometric Equations Involving Special Angles Mathematics

Find the measure of βˆ π‘‹ in degrees given 2 cos 𝑋 = tan 60Β° where 𝑋 is an acute angle.

01:34

Video Transcript

Find the measure of angle 𝑋 in degrees given that two times cos of 𝑋 equals the tan of 60 degrees, where 𝑋 is an acute angle.

Since 𝑋 is an acute angle, we’re only interested in solutions in quadrant one. So, we can look at two times cos of 𝑋 is equal to tan of 60 degrees. And the first thing that we can do is solve for tan of 60 degrees, which is equal to the square root of three. Because this is an angle that we usually memorize, you maybe already knew that the tan of 60 degrees was the square root of three. If not, you could plug that into your calculator. Now, we have two times cos of 𝑋 equals the square root of three. Our goal is to solve for 𝑋. We’re trying to get 𝑋 by itself. So, we divide through by two and we see that the cos of 𝑋 has to equal the square root of three over two.

And one of two things can happen here. You might remember that the cos of 30 degrees is the square root of three over two. Or you might recognize that we can solve for 𝑋 by finding the inverse cosine of both sides of this equation. The inverse cos of the cos of 𝑋 equals π‘₯ and the inverse cos of the square root of three over two can be plugged into a calculator, which will return 30 degrees. If you knew that the cos of 30 degrees was the square root of three over two, you would recognize that 𝑋 has to be equal to 30 degrees. But both methods prove this.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.