Question

If possible, find the exact value of
sec[arctan(-5)]. Pls explain steps to solve such questions....

Answer 1

arctan means inverse of the tangent function.\[\tan ^{-1}\]is another way of writing arctan (inverse of tan). If\[arc \tan y =\theta \]for example, then\[y =\tan \theta \]Do you understand? If this clue helps, then what do you think is the first step towards your problem?

Answer 2

that way I will get -5 = tan A (i am using A for ease of typing here)...then what???? Do I draw a right triangle??? In which quadrant???

Answer 3

If possible pls explain this question with full step by step solution so that I can go through it and get to know how to solve such sums...This is one of the few I could not do....

Answer 4

Example:
Find the exact value of\[\sin (arc \cos 0.8)\]
Solution:
First let arc cos 0.8 = θ, this implies that cos θ = 0.8 = 4/5. Now

sin²θ + cos²θ = 1

sin²θ + (4/5)² = 1 [∵ cos θ = 4/5]

sin²θ + (16/25) = 1

sin²θ = 1 - (16/25)

sin²θ = 9/25

sin θ = ± 3/5

We reject -3/5 because cos θ was positive.

sin θ = 3/5

∴ sin (arc cos 0.8) = 3/5

Answer 5

You could have also drawn a triangle.

From which you see that sin θ = 3/5.

Thus you may use either the identities or the triangle.