How do you find the exact value of Sin 45degrees + cos 60degrees?

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How do you find the exact value of Sin 45degrees + cos 60degrees?

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Answer 1 · 2015-07-17T21:39:21

$\frac{\sqrt{2}}{2} + \frac{1}{2}$ $sqrt2/2+1/2$

Explanation:

Recall the unit circle:

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From the unit circle we can see that at $45^{o}$ $45^o$ the position of the angle on the unit circle is at $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$ $(sqrt2/2,sqrt2/2)$

$(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}) = (cos θ, sin θ)$ $(sqrt2/2,sqrt2/2)=(costheta,sintheta)$

So, for $45^{o}$ $45^o$ , $sin (45^{o}) = \frac{\sqrt{2}}{2}$ $sin(45^o)=sqrt2/2$

Now, from the unit circle we can see that at $60^{o}$ $60^o$ the position of the angle on the unit circle is at $(\frac{1}{2}, \frac{\sqrt{3}}{2})$ $(1/2,sqrt3/2)$

$(\frac{1}{2}, \frac{\sqrt{3}}{2}) = (cos θ, sin θ)$ $(1/2,sqrt3/2)=(costheta,sintheta)$

So, for $60^{o}$ $60^o$ , $cos (60^{o}) = \frac{1}{2}$ $cos(60^o)=1/2$

So,

$sin (45^{o}) + cos (60^{o}) = \frac{\sqrt{2}}{2} + \frac{1}{2}$ $sin(45^o)+cos(60^o)=sqrt2/2+1/2$

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How do you find the exact value of Sin 45degrees + cos 60degrees?

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