Answer to Question #144319 in Trigonometry for Shahir Sheikh

Question

If sec(α)<0 and sin(α)=15/17,

what quadrant is the terminal side of α in?

Answer 1

From the trignometric sign conventation :

• Sine is positive in first quadratnt
• Sine is positive in second quadratnt
• Sine is negative in third quadratnt
• Sine is negative in fourth quadratnt
• In the question value of sine is positive so it can lie either in the first or second quadrant

From the trigonometric sign conventation :

• Cosine is positive in first quadratnt
• Cosine is negative in second quadratnt
• Cosine is negative in third quadratnt
• Cosine is positive in fourth quadratnt
• As we know that reciprocal of cosine is secant.
• In the question secant is negative thus it can be either in the second or third quadranr

But sine is positive in positive and secant is negative so angle alpha should be definitely in the second quadrant.