Question

find the value of tan( - 1590 )degree

Answer 1

Find the attachment
Concept used
Tan(-x) = -Tanx
In second quad, tan is negative
Odd multiple, t - ratio change

Answer 2

Concept

Trigonometry is a branch of mathematics that is concerned with specific functions of angles and their application to calculations. To solve this question we need to know the trigonometric identities specifically the one- tan(90-x) = cot(x)

Find

we are asked to find the value of tan(-1590) degrees

Solution

We can write tan(-1590) as,

tan(-1590) = -tan(1590)

= - tan {( 90 * 17) + 60}

= - tan {( 90 * 17) - (-60)}

= - { cot(-60) }

= cot(60)

Now, from the trigonometric tables, we can find the value of cot(60) degrees which is $1/\sqrt{3}$

⇒ cot(60) = $1/\sqrt{3}$

Thus, the value of tan(-1590) degrees is $1/\sqrt{3}$

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