# Find the values of sinx, tanx, secx, and cscx if cosx = 0.23

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We have cos x = .23

sin x = sqrt (1 - (cos x)^2) = sqrt ( 1 - .23^2) = .9731

tan x = sin x / cos x = .973 / .23 = 4.2312

sec x = 1/ cos x = 1/ .23 = 4.3478

cosec x = 1/ sin x = 1/ .973 = 1.0277

Given cos(x) = 0.23

We need to find sin(x), tan(x) , sec(x), and (csc(x).

First, we know that sec(x) = 1/cos(x).

==> sec(x) = 1/(0.23) = 4.3478.

**==> sec(x) = 4.3478.**

Now we will use the trigonometric identities to find sin(x).

We know that:

sin^2 x + cos^2 x = 1

==> sin(x) = sqrt(1-cos^2x)

= sqrt(1-0.23^2)

= sqrt(0.9471)

= 0.9732

**==> sin(x) = 0.9732.**

Now we know that csc(x) = 1/sin(x)

==> csc(x) = 1/(0.9732) = 1.0275

**==> csc(x) = 1.0275**

Now we know that tan(x) = sin(x)/ cos(x).

==> tan(x) = 0.9732/ 0.23 = 4.2313

**==> tan(x) = 4.2313**

cosx = 0.23.

Therefore sinx = +or- sqrt(1-cos^2x) = +or- sqrt(1-0.23)^2

sinx = + or - 0.9732 nearly.

tanx = sinx/cosx = + or- (0.9732/0.23) = 4.23.

sex = 1/cosx = 1/0.23 = 4.3478.

cosecx = 1/sinx = +or- (1/0.9732) = +or- 1.0275.