Question

Suppose that \(\theta\) is an acute angle of a right triangle and that \(\sec(\theta) = \frac{5}{2}\). Find \(\cos(\theta)\) and \(\csc(\theta)\). \(\circ \cos(\theta) = \frac{5\sqrt{21}}{21}, \csc(\theta) = \frac{\sqrt{21}}{2}\) \(\circ \cos(\theta) = \frac{2}{5}, \csc(\theta) = \frac{\sqrt{21}}{5}\) \(\circ \cos(\theta) = \frac{2}{5}, \csc(\theta) = \frac{5\sqrt{21}}{21}\) \(\circ \cos(\theta) = \frac{\sqrt{21}}{5}, \csc(\theta) = \frac{2\sqrt{21}}{21}\) \(\circ \cos(\theta) = \frac{5}{2}, \csc(\theta) = \frac{5\sqrt{21}}{21}\)

          Suppose that \(\theta\) is an acute angle of a right triangle and that \(\sec(\theta) = \frac{5}{2}\). Find \(\cos(\theta)\) and \(\csc(\theta)\).

\(\circ \cos(\theta) = \frac{5\sqrt{21}}{21}, \csc(\theta) = \frac{\sqrt{21}}{2}\)

\(\circ \cos(\theta) = \frac{2}{5}, \csc(\theta) = \frac{\sqrt{21}}{5}\)

\(\circ \cos(\theta) = \frac{2}{5}, \csc(\theta) = \frac{5\sqrt{21}}{21}\)

\(\circ \cos(\theta) = \frac{\sqrt{21}}{5}, \csc(\theta) = \frac{2\sqrt{21}}{21}\)

\(\circ \cos(\theta) = \frac{5}{2}, \csc(\theta) = \frac{5\sqrt{21}}{21}\)
        
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Suppose that θ is an acute angle of a right triangle and that sec(θ) = (5)/(2). Find cos(θ) and csc(θ).

∘cos(θ) = (5√(21))/(21), csc(θ) = (√(21))/(2)

∘cos(θ) = (2)/(5), csc(θ) = (√(21))/(5)

∘cos(θ) = (2)/(5), csc(θ) = (5√(21))/(21)

∘cos(θ) = (√(21))/(5), csc(θ) = (2√(21))/(21)

∘cos(θ) = (5)/(2), csc(θ) = (5√(21))/(21)

Added by Tara C.

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Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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Suppose that heta is an acute angle of a right triangle and that sec( heta )=(5)/(2). Find cos( heta ) and csc( heta ). cos( heta )=(5sqrt{21})/(21), csc( heta )=(sqrt{21})/(2) cos( heta )=(2)/(5), csc( heta )=(sqrt{21})/(5) cos( heta )=(2)/(5), csc( heta )=(5sqrt{21})/(21) cos( heta )=(sqrt{21})/(5), csc( heta )=(2sqrt{21})/(21) cos( heta )=(5)/(2), csc( heta )=(5sqrt{21})/(21)
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Transcript

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00:02 Okay, we're given that the cosine of an angle is the square root of 21 over 7, and we're being asked to find the cosecant of that angle, which i just wrote a note that cosecant is the hypotenuse over opposite when you have a right triangle because it's the inverse of sine.
00:26 I mean, it's the reciprocal of sine.
00:28 So let me draw a just generic right triangle to represent our angle.
00:40 So let's say our angle is theta here.
00:47 So if the cosine is square root of 21 over 7, remember cosine was adjacent over hypotenuse, then i can call this adjacent sine square root of 21 and this hypotenuse is 7, and that could represent our trig ratio.
01:16 So now for cosecant, we know the hypotenuse, but we don't know the opposite side.
01:28 Let's call that x over here.
01:31 So we can solve for x using the pythagorean theorem because we know that square root of 21 squared plus x squared is going to equal 7 squared.
01:49 Hmm, see i'm out of room over here.
01:55 Let me rewrite that.
01:57 So square root of 21 squared plus x squared equals 7 squared.
02:05 And let me delete this here...
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