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Question

# In each of the following, one of the six stigonometric ratios is given. Find the values of the other trigonometric ratios. (i) sin A=23 (ii) cos A=45 (iii) tan θ=11 (iv) sin θ=1115 (v) tan α=512 (vi) sin θ=√32 (vii) cos θ=725 (viii) tan θ=815 (ix) cot θ=125 (x) sec θ=135 (xi) cosec θ=√10 (xii) cos θ=1215

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Solution

## (i) cos A=√53,tan A=2√5,sec A=3√5,cosec A=32,cot A√52 (ii) sin A=35,tan A=34,sec A=54,cosec A=53,cot A=43 (iii) sin θ=11√122,cosθ=1√122,cosecθ=√12211,secθ=√122,cotθ=111 (iv) cos θ=2√2615,tan θ=112√26,sec A=152√26,cotθ=2√2611,cosecθ=1511 (v) sin α=513,cos α=1213,cot α=125,cosec α=135,secα=1312 (vi) cos θ=12,tan θ=√3, sec θ=2, cosec θ=2√3, cot θ=1√3 (vii) sin θ=2425, tan θ=247,sec θ=257, cosec θ=2524, cot θ=724 (viii) sin θ=817, cos θ=1517, cot θ=158, cosec θ=178, sec θ=1715 (ix) tan θ=512, sin θ=513, cos θ=1213, cosec θ=135,sec θ=1312 (x) sin θ=1213, cos θ=513. tan θ=125, cosec θ=1312, cot θ=512 (xi) sin θ=1√10, cos θ=3√10, tan θ=13, sec θ=√103, cot θ=3 (xii) sin θ=915, tan θ=912, cosec θ=159, cot θ=129, sec θ=1512

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