A triangle has two corners of angles #(3pi )/8# and #(7pi)/12 #. What are the complement and supplement of the third corner?
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To find the complement and supplement of the third angle in the triangle, first, we need to find the measure of the third angle. Since the sum of the angles in a triangle is always 180 degrees (π radians), we can use this information to find the measure of the third angle.
Let x be the measure of the third angle.
Given that the two angles are (3π)/8 and (7π)/12, we can write the equation:
(3π)/8 + (7π)/12 + x = π
Now, solve for x:
(3π)/8 + (7π)/12 + x = π => (9π + 7π + 8x) / 24 = π => (16π + 8x) / 24 = π => 16π + 8x = 24π => 8x = 8π => x = π
So, the measure of the third angle is π radians.
Now, to find the complement and supplement:
Complement of an angle = π/2 - angle measure => Complement of the third angle = π/2 - π = π/2 - π = -π/2 (or 90° - 180°)
Supplement of an angle = π - angle measure => Supplement of the third angle = π - π = π (or 180°)
Therefore, the complement of the third angle is -π/2 radians (or 90 degrees), and the supplement of the third angle is π radians (or 180 degrees).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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