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Question

If tanA=3 find values of all other trigonometric ratios.


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Solution

Step 1: Solve for the value of cotA

Given, tanA=3

Since tanA is positive in first or third quadrant so only cotA will be positive rest all trigonometric ratios can have positive as well as negative values.

tanA=3cotA=1tanAcotA=13

Step 2: Solve for the value of secA

secA=1+tan2Asec2A-tan2A=1secA=±2

Step 3: Solve for the value of cosA

cosA=1secAcosA=±12

Step 4: Solve for the value of sinA

sinA=1-cos2Asin2A+cos2A=1sinA=±32

Step 5: Solve for the value of cscA

cosecA=1sinAcosecA=±23

Hence the values of all the trigonometric ratios are:

sinA=±32cosA=±12tanA=3cscA=±23secA=±2cotA=13


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