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Q 1 PLEASE HELP ME FIGURE THIS OUT 1.0

Q 1 PLEASE HELP ME FIGURE THIS OUT 1.0-example-1
Q 1 PLEASE HELP ME FIGURE THIS OUT 1.0-example-1
Q 1 PLEASE HELP ME FIGURE THIS OUT 1.0-example-2
User Jonathan W
by
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1 Answer

5 votes

Answer:
(2√(2)-√(3))/(2)

Step-by-step explanation (using the Unit Circle):

csc
(\pi)/(4) - cos
(\pi)/(6)

csc =
(1)/(sin)

sin
(\pi)/(4) =
(√(2))/(2)

→ csc
(\pi)/(4) =
(2)/(√(2))=
{√(2)}

cos
(\pi)/(6) =
(√(3))/(2)

csc
(\pi)/(4) - cos
(\pi)/(6)

=
{√(2)} -
(√(3))/(2)

=
{√(2)}*((2)/(2)) -
(√(3))/(2)

=
(2√(2))/(2) -
(√(3))/(2)

=
(2√(2)-√(3))/(2)

Step-by-step explanation (using the special triangles):


(\pi)/(4) = 45°

a 45°-45°-90° triangle has sides with proportions of: 1 - 1 - √2

csc =
(hypotenuse)/(opposite) =
\frac{√(2)} {1} =√(2)


(\pi)/(6) = 30°

a 30°-60°-90° triangle has sides with proportions of: 1 - √3 - 2

cos =
(adjacent)/(hypotenuse) =
(√(3))/(2)

csc
(\pi)/(4) - cos
(\pi)/(6) =
\frac{2√(2)-√(3)} {2}

*****************************************************************************************

Answer: secθ

Explanation:

cosθ csc²θ tan²θ

= cosθ *
(1)/(sin^(2)\theta) *
\frac{sin^(2)\theta} {cos^(2)\theta}

=
(1)/(cos\theta)

= secθ

User Inafalcao
by
6.0k points