The point is on the terminal side of an angle in standard position.Determine the exact values of the three trigonometric functions sine,cosine,and tangent of the angle θ. $( 15,8 )$
A)sin θ = $\frac { 8 } { 17 }$ cos θ = $\frac { 8 } { 15 }$
Tan θ = $\frac { 15 } { 17 }$
B)sin θ = $\frac { 8 } { 15 }$ cos θ = $\frac { 15 } { 17 }$
Tan θ = $\frac { 8 } { 17 }$
C)sin θ = $\frac { 15 } { 17 }$ cos θ = $\frac { 8 } { 17 }$
Tan θ = $\frac { 8 } { 15 }$
D)sin θ = $\frac { 8 } { 17 }$ cos θ = $\frac { 15 } { 17 }$
Tan θ = $\frac { 8 } { 15 }$
E)sin θ = $\frac { 8 } { 17 }$ cos θ = $\frac { 15 } { 17 }$
Tan θ = $\frac { 8 } { 17 }$

Question

The point is on the terminal side of an angle in standard position.Determine the exact values of the three trigonometric functions sine,cosine,and tangent of the angle θ.​ $( 15,8 )$ ​
A)sin θ = $\frac { 8 } { 17 }$ cos θ = $\frac { 8 } { 15 }$
Tan θ = $\frac { 15 } { 17 }$
B)sin θ = $\frac { 8 } { 15 }$ cos θ = $\frac { 15 } { 17 }$
Tan θ = $\frac { 8 } { 17 }$
C)sin θ = $\frac { 15 } { 17 }$ cos θ = $\frac { 8 } { 17 }$
Tan θ = $\frac { 8 } { 15 }$
D)sin θ = $\frac { 8 } { 17 }$ cos θ = $\frac { 15 } { 17 }$
Tan θ = $\frac { 8 } { 15 }$
E)sin θ = $\frac { 8 } { 17 }$ cos θ = $\frac { 15 } { 17 }$
Tan θ = $\frac { 8 } { 17 }$

Quizplus · Accepted Answer

The point (15, 8) suggests a right triangle with legs of 15 (adjacent to the angle) and 8 (opposite the angle), and the hypotenuse can be found using the Pythagorean theorem: $\sqrt{15^2 + 8^2} = \sqrt{225 + 64} = \sqrt{289} = 17$. Therefore, $\sin \theta = \frac{opposite}{hypotenuse} = \frac{8}{17}$, $\cos \theta = \frac{adjacent}{hypotenuse} = \frac{15}{17}$, and $\tan \theta = \frac{opposite}{adjacent} = \frac{8}{15}$.

The Point Is on the Terminal Side of an Angle (15,8)( 15,8 )(15,8)

The Point Is on the Terminal Side of an Angle $( 15,8 )$