<p>Hi everyone,</p>
<p>I am working my way through Barron's SAT Physics book and am really surprised that they do use more complex calculations that include cos and sin. They are not difficult, but without a calculator, I mean, how am I supposed to know all the values of sin and cos and use them in my calculations?!</p>
<p>I hope you can shed some light!</p>
<p>Thank you very much</p>
<p>Mrmaster</p>
<p>You should at least know sine and cosine of angles that are multiples of π/6 and π/4. This requires knowing the 30-60-90 and 45-45-90 triangles.</p>
<p>To find sin(π/3) quickly in your head, visualize a unit circle with a terminal angle of π/3 (60 deg). The ray corresponding to pi/3 will intersect the unit circle at some point. </p>
<p>The sine of the angle is simply the y-coordinate of that point (sin θ = y/r = y because r = 1). The cosine of the angle is the x-coordinate of that point. For π/3, the corresponding point on the unit circle is (1/2, √3/2), so cos (π/3) = 1/2.</p>
<p>In general, for a unit circle with radius r = 1,
sin θ = y
cos θ = x
tan θ = y/x.</p>
<p>Thank you very much, rspence!</p>