question 21 (1 point)\nthe point (3, 4) is on the terminal arm of da. which is the set of exact primary…

question 21 (1 point)\nthe point (3, 4) is on the terminal arm of da. which is the set of exact primary trigonometric ratios for the angle?\no a) sin a = 4/5, cos a = 3/5, tan a = 3/4\no b) sin a = 5/4, cos a = 5/3, tan a = 3/4\no c) sin a = 3/5, cos a = 4/5, tan a = 4/3\no d) sin a = 4/5, cos a = 3/5, tan a = 4/3
Answer
Explanation:
Step1: Calculate the hypotenuse ( r )
Using the Pythagorean theorem ( r=\sqrt{x^{2}+y^{2}} ), where ( x = 3 ) and ( y = 4 ). ( r=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5 )
Step2: Calculate ( \sin A )
( \sin A=\frac{y}{r} ), substituting ( y = 4 ) and ( r = 5 ) ( \sin A=\frac{4}{5} )
Step3: Calculate ( \cos A )
( \cos A=\frac{x}{r} ), substituting ( x = 3 ) and ( r = 5 ) ( \cos A=\frac{3}{5} )
Step4: Calculate ( \tan A )
( \tan A=\frac{y}{x} ), substituting ( y = 4 ) and ( x = 3 ) ( \tan A=\frac{4}{3} )
Answer:
D. ( \sin A=\frac{4}{5},\cos A=\frac{3}{5},\tan A=\frac{4}{3} )