Diketahui cos = - [tex] \frac{15}{25} [/tex], α dikuadran 3. Tentukan nilai dari : a. tan α b. sin α c. cot²α - cosec²α

cos α= - 15/25 → dimana cos α= x/r
pd kuadran III

sisi depan sudut :
y²= 25² - 15²
y²= 625 - 225
y²= 400
y= 20

a. tan α
= y / x
= 20/15
= 4/3

b. sin α
= y / r
= 20/25
= - 4/5

c. cot²α - cosec²α
nilai cot α= 1/tan α= 3/4
nilai cosec α= 1/sin α= - 5/4

maka,
= (cot α + csc α)(cot α - csc α)
= (3/4 + (- 5/4))(3/4 - (- 5/4))
= (3/4 - 5/4)(3/4 + 5/4)
= 9/16 + 15/16 - 15/16 - 25/16
= 9/16 - 25/16
= - 16/16= -1

*cmiiw

Bab Trigonometri
Matematika SMA Kelas X

kuadran III
b] sin a = √(1 - cos² a)
sin a = √(1 - (-15/25)²)
sin a = √(1 - 225/625)
sin a = √(400/625)
sin a = 20/25
karena di kuadran III,
sin a = -20/25

a] tan a = sin a / cos a
tan a = (-20/25) / (-15/25)
tan a = (-20/25) x (-25/15)
tan a = 20/15

c] cot² a - cosec² a
= cot² a - (cot² a + 1)
= -1