The value of sine theta = negative eight-seventeenths ⇒ 2nd
Step-by-step explanation:
Let us revise the quadrant of an angle its terminal side passes through a given point
- If the given point is (x , y), then the angle lies in the 1st quadrant
- If the given point is (-x , y), then the angle lies in the 2nd quadrant
- If the given point is (-x , -y), then the angle lies in the 3rd quadrant
- If the given point is (x , -y), then the angle lies in the 4th quadrant
∵ The terminal side of angle Ф passes through P (15 , -8)
∵ x = 15 and y = -8
- P is (x , -y), then the angle Ф lies in the 4th quadrant
∵ The terminal side of angle Ф is the hypotenuse of a right
triangle whose horizontal leg is 15 units and vertical leg
is -8 units
- Use Pythagoras Theorem to find the length of the hypotenuse
∴ Hypotenuse = [tex]\sqrt{(15)^{2}+(-8)^{2}}=17[/tex] units
∵ sinФ = [tex]\frac{opposite}{hypotenuse}[/tex]
∵ The side opposite to Ф is -8
∵ The hypotenuse is 17
∴ sinФ = [tex]\frac{-8}{17}[/tex]
The value of sine theta = negative eight-seventeenths
Learn more:
You can learn more about the trigonometry function in brainly.com/question/4924817
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