Question

If sin Ɵ - √3 cos Ɵ=0 and 0˚<Ɵ <90˚, find the value of Ɵ.​

Answer 1

Question:-

• If sin Ɵ - √3 cos Ɵ=0 and 0˚<Ɵ <90˚, find the value of Ɵ.

Solution:-

We have

⇒sin Ɵ - √3 cos Ɵ=0

⇒sin Ɵ = √3 cos Ɵ

⇒sin Ɵ /cos Ɵ=√3

⇒tan Ɵ=√3

Using trignometric ratio table

tan Ɵ=tan 60⁰

⇒ Ɵ=60⁰

More to know about trignometric ratio table :-

• ➠sin 0⁰ =0
• ➠sin 30⁰=1/2
• ➠sin 45⁰=1/√2
• ➠sin 60⁰=√3/2
• ➠sin 90⁰= 1

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• ➠cos 0⁰ =1
• ➠cos 30⁰=√3/2
• ➠cos 45⁰=1/√2
• ➠cos 60⁰=1/2
• ➠cos 90⁰= 0

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• ➠tan 0⁰ =0
• ➠tan 30⁰=1/√3
• ➠tan 45⁰=1
• ➠tan 60⁰=√3
• ➠tan 90⁰= not defined

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• ➠cosec 0⁰ =not defined
• ➠cosec 30⁰=2
• ➠cosec 45⁰=√2
• ➠cosec 60⁰=2/√3
• ➠cosec 90⁰= 1

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• ➠sec 0⁰ =1
• ➠sec 30⁰=2/√3
• ➠sec 45⁰=√2
• ➠sec 60⁰=2
• ➠sec 90⁰= not defined

--------------------------------------

• ➠cot 0⁰ =not defined
• ➠cot 30⁰=√3
• ➠cot 45⁰=1
• ➠cot 60⁰=1/√3
• ➠cot 90⁰= 0

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