SOLUTION: One of the primary trigonometric ratios for an angle is given, as well as the quadrant that the terminal arm lies in. Determine the other two primary trigonometric ratios. a) sin

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Question 1161053: One of the primary trigonometric ratios for an angle is given, as well as the quadrant that the terminal arm lies in. Determine the other two primary trigonometric ratios.
a) sin A = 4/5, first quadrant
b) cos B = 8/17, fourth quadrant
c) tan C = -12/5, second quadrant
Found 3 solutions by math_helper, solver91311, MathTherapy:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
I worked out (a) and (b), you can do (c) by following the same template. Just rmemeber when you do part (c): for Q2, cos and tan are < 0, sin > 0



Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!











and then



==================================

Similarly, given





and




==================================
















or











In all cases, select the sign based on the quadrant of the terminal ray of the angle.

Sine is positive in QI and QII

Cosine is positive in QI and QIV

Tangent is positive in QI and QIII


John

My calculator said it, I believe it, that settles it
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
One of the primary trigonometric ratios for an angle is given, as well as the quadrant that the terminal arm lies in. Determine the other two primary trigonometric ratios.
a) sin A = 4/5, first quadrant
b) cos B = 8/17, fourth quadrant
c) tan C = -12/5, second quadrant 
The 3 primary TRIG. RATIOS are sin, cos, and tan

a) 

   This represents one of the many PYTHAGOREAN TRIPLES, as this is a 3-4-5 right triangle.

   And, with ∡A being in the 1st quadrant, where ALL RATIOS are POSITIVE (+), and y being 4, r being 5, we get "x" to be 3.

   The other 2 TRIG. RATIOS are: 

b) Let me GUIDE you!

   

   This represents one of the many PYTHAGOREAN TRIPLES, as this is an 8-15-17 right triangle.

   And, with ∡B being in the 4th quadrant, where ONLY "cos" is POSITIVE (+), and x being 8, r being 17, we get "y" to be - 15.

   The other 2 TRIG. RATIOS are:  <======= Fill in the MISSING pieces!

c) Let me GUIDE you!

   

   This represents one of the many PYTHAGOREAN TRIPLES, as this is a 5-12-13 right triangle.

   And, with ∡C being in the 2nd quadrant, where ONLY "sin" is POSITIVE (+), and x being - 5, y being 12, we get "r" to be 13.

   The other 2 TRIG. RATIOS are:  <======= Fill in the MISSING pieces! 

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