"If cos(θ)= 8/17 and 0°<θ<90°, what is sec(θ)? Write your answer in simplified, rationalized form. sec(θ)= ______"

Identify Relation: Identify the relation between cos(θ) and sec(θ). sec(θ) is the reciprocal of cos(θ). sec(θ) = 1 / cos(θ)Reciprocal Relation: We know: sec(θ) = 1 / cos(θ) cos(θ) = 8 / 17 Identify the equation of sec(θ) after substituting 8 / 17 for cos(θ). sec(θ) = 1 / cos(θ) sec(θ) = 1 / (8 / 17)Substitute Cosine: sec(θ) = 1 / (8 / 17) Find the value of sec(θ). sec(θ) = 1 / (8 / 17) sec(θ) = 1 * (17 / 8) sec(θ) = 17/8

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If $\cos(\theta) = \frac{8}{17}$ and 0^\circ < \theta < 90^\circ , what is $\sec(\theta)$ ? $\newline$ Write your answer in simplified, rationalized form. $\newline$ $\sec(\theta) =$ ______

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Precalculus

Find trigonometric ratios using a Pythagorean or reciprocal identity

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Q. If

\cos(\theta) = \frac{8}{17}

and

0^\circ < \theta < 90^\circ

, what is

\sec(\theta)

\newline

Write your answer in simplified, rationalized form.

\newline

\sec(\theta) =

______

Identify Relation: Identify the relation between $\cos(\theta)$ and $\sec(\theta)$ . $\newline$ $\sec(\theta)$ is the reciprocal of $\cos(\theta)$ . $\newline$ $\sec(\theta) = \frac{1}{\cos(\theta)}$
Reciprocal Relation: We know: $\newline$ $\sec(\theta) = \frac{1}{\cos(\theta)}$ $\newline$ $\cos(\theta) = \frac{8}{17}$ $\newline$ Identify the equation of $\sec(\theta)$ after substituting $\frac{8}{17}$ for $\cos(\theta)$ . $\newline$ $\sec(\theta) = \frac{1}{\cos(\theta)}$ $\newline$ $\sec(\theta) = \frac{1}{(\frac{8}{17})}$
Substitute Cosine: $\sec(\theta) = 1 / (8 / 17)$ $\newline$ Find the value of $\sec(\theta)$ . $\newline$ $\sec(\theta) = 1 / (8 / 17)$ $\newline$ $\sec(\theta) = 1 \times (17 / 8)$ $\newline$ $\sec(\theta) = 17/8$