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Write the first trigonometric function in terms of the second for in the given quadrant. (No theta symbol so used word)

sec(theta), tan(theta); theta in Quadrant IV

sec(theta) =


Sagot :

The expression of [tex] \mathbf{sec( \theta)}[/tex] in terms of [tex]tan( \theta)[/tex] in Quadrant IV is presented as follows;

[tex] sec( \theta) = \sqrt{{tan( \theta)}^{2} + 1} [/tex]

Which trigonometric identity can be used to express the required function?

The given trigonometric functions are;

[tex]sec( \theta)[/tex]

[tex]tan( \theta)[/tex]

[tex] {sec( \theta)}^{2} = {tan( \theta)}^{2} + 1[/tex]

In Quadrant IV, the tangent of an angle is -ve, while the secant is +ve

However, the square of -ve is positive;

  • (-ve)² = +ve

Therefore;

[tex] \left({tan( \theta)}^{2} + 1 \right) \: is \: positive[/tex]

Which gives;

  • [tex] sec( \theta) = \sqrt{{tan( \theta)}^{2} + 1} [/tex]

Learn more about regular trigonometric identities here:

https://brainly.com/question/12335464

#SPJ1

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