X = -3
y = 3*sqrt(3)
r = sqrt(x^2 + y^2)
r = sqrt((-3)^2 + (3*sqrt(3))^2)
<span>r = sqrt(9+27)
</span><span>r = sqrt(36)
</span>r = 6
theta = arctan(y/x)
<span>theta = arctan(3sqrt(3)/(-3))
</span>theta = arctan(-sqrt(3))
theta = -60 degrees which is coterminal to 300 degrees
So the polar form is (r,theta) = (6, 300)
Find the 10th term in the following arithmetic sequence if the constant being added is -12
Step-by-step explanation:
20 - 12 = 8
8 - 12 = -4
-4 - 12 = -16
So the sequence will be
20; 8; -4; -16
an = 20 - 12(n - 1)
a10 = 20 - 12(10 - 1) = -88
<span><span>(<span>sinx</span>−<span>tanx</span>)</span><span>(<span>cosx</span>−<span>cotx</span>)</span></span>
<span>=<span>(<span>sinx</span>−<span><span>sinx</span><span>cosx</span></span>)</span><span>(<span>cosx</span>−<span><span>cosx</span><span>sinx</span></span>)</span></span>
<span>=<span>sinx</span><span>(1−<span>1<span>cosx</span></span>)</span><span>cosx</span><span>(1−<span>1<span>sinx</span></span>)</span></span>
<span>=<span>sinx</span><span>(<span><span>cosx</span><span>cosx</span></span>−<span>1<span>cosx</span></span>)</span><span>cosx</span><span>(<span><span>sinx</span><span>sinx</span></span>−<span>1<span>sinx</span></span>)</span></span>
<span>=<span><span>sinx</span><span>cosx</span></span><span>(<span>cosx</span>−1)</span><span><span>cosx</span><span>sinx</span></span><span>(<span>sinx</span>−1)</span></span>
<span>=<span>(<span>cosx</span>−1)</span><span>(<span>sinx</span>−1<span>)</span></span></span>
