True or False

Algebra Level 2

If a=160 degree, then sin a+ cos a > 0, true or false?

Can't say True False None

Agr Amul by Agr Amul , 21, India

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1 solution

Ganesh Ayyappan
Dec 8, 2014

sin 160 + cos 160 = cos 70 + (- sin 70) [ using "sin (90 + A) = + cos A" and "cos (90 + A) = - sin A" ]

cos 70 - sin 70 = sin 20 - sin 70 [ since "cos (90 - A) = sin A"]

now sin 20 < sin 70 ..... (since "sin" value increases with A ) ......... hence the answer

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You could use the following to improve the appearance of your problem:

If a = 16 0 ∘ a=160^\circ , then sin ⁡ a + cos ⁡ a > 0 \sin a+\cos a > 0 , true or false?

Marta Reece - 3 years, 2 months ago

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