Question

Question 28
Let be an angle in quadrant such that.
Find the exact values of and.

Answer 1

Answer:

see explanation

Step-by-step explanation:

Since Θ is an angle in the third quadrant, then secΘ < 0 and tanΘ > 0

Using the identity

sec x = $\frac{1}{cosx}$ , then

cos x = - $\sqrt{1-sin^2x}$

         = - $\sqrt{1-(-3/5)^2}$ = - $\sqrt{1-\frac{9}{25} }$ = - $\sqrt{\frac{16}{25} }$ = - $\frac{4}{5}$, thus

secΘ = $\frac{1}{-\frac{4}{5} }$ = - $\frac{5}{4}$

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Using the identity

tan x = $\frac{sinx}{cosx}$ , then

tanΘ = $\frac{-\frac{3}{5} }{-\frac{4}{5} }$ = - $\frac{3}{5}$ × - $\frac{5}{4}$ = $\frac{3}{4}$

Answer 2

The value of sec(x) is (5/4) and tan(x) will be (-3)(4).

What is trigonometry?

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.

Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios.

The six trigonometric ratios are the source of all fundamental trigonometric identities.

The given value of sin (x) is ( -3 / 5 ). The values of sec(x) and tan(x) will be calculated as below:-

sec(x) = 1 / cos(x)

$cosx = \sqrt{1-sin^2x}$

$cosx = \sqrt{1-(\dfrac{-3}{5})^2}$

cos(x) = 4 / 5

sec(x) = 1 / ( 4 / 5 ) = ( 5/ 4)

The value of tan(x) will be calculated as:-

tan(x) = sin(x)/cos(x) = ( -3 / 5 ) / (4 / 5 )

tan(x) = (-3/4)

Therefore, the value of sec(x) is (5/4) and tan(x) will be (-3)(4).

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