Find the exact value of trigonometric function of angle theta if theta is an angle in standard position whose terminal side contains the given point (21,28) find sin theta
To find the sine of angle theta, we first need to determine the values of the opposite side, adjacent side, and hypotenuse of the triangle formed by the given point (21, 28).
Using the distance formula, we can find the length of the hypotenuse:
hypotenuse = √(21² + 28²) = √(441 + 784) = √1225 = 35
Now, we can find the sine of angle theta using the definition of sine: sin(theta) = opposite side / hypotenuse.
Using the Pythagorean theorem, we can find the opposite side:
opposite side = √(hypotenuse² - adjacent side²) = √(35² - 21²) = √(1225 - 441) = √784 = 28
Therefore, sin(theta) = opposite side / hypotenuse = 28 / 35 = 4 / 5.
So, the exact value of sin(theta) is 4/5.