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Ad libitum [116K]
3 years ago
9

Or an angle θ with the point (−20, −21) on its terminating side, what is the value of cosine?

Mathematics
2 answers:
coldgirl [10]3 years ago
5 0

Answer:

The value of cosine is \cos \theta=-\frac{20}{29}.

Step-by-step explanation:

It is given that an angle θ with the point (−20, −21) on its terminating side.

It means the right angle triangle is formed in third quadrant where length of the perpendicular is 21 and the base is 20.

According to the Pythagoras theorem,

hypotenuse^2=base^2+perpendicular^2

hypotenuse^2=(20)^2+(21)^2

hypotenuse^2=400+441

hypotenuse^2=841

Taking square root both the sides.

hypotenuse=\sqrt{841}

hypotenuse=29

In a right angled triangle,

\cos \theta=\frac{base}{hypotenuse}

\cos \theta=\frac{20}{29}

θ lie in the third quadrant and cosine is negative in third quadrant.

\cos \theta=-\frac{20}{29}

Therefore the value of cosine is \cos \theta=-\frac{20}{29}.

kherson [118]3 years ago
3 0
Cos(θ) = -20/√((-20)^2 +(-21)^2)
.. = -20/-√841 . . . . . . . . . . . . . . . . . θ is a 4th-quadrant angle, so cos(θ) > 0
.. = 20/29

The value of the cosine is 20/29.
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