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Question:

Find the value of other five trigonometric ratios when sinx = 3/5, and x lies in the second quadrant.

Solution:

sinx=3/5 ⇒cscx=1/sinx=5/3
∵sin²x+cos²x=1 ⇒cos²x=1−sin²x=1−(3/5)²=1−9/25=16/25
⇒cosx=±4/5
Since x lies in the second quadrant, the value of cosx will be negative
∴cosx=−4/5
∴secx=1/cosx=−5/4
tanx=sinx/cosx=(3/5)/(−4/5)=−3/4
cotx=1/tanx=−4/3