Chetan wants to make a necklace with 50 beads. He knows that 12 beads take up 5 inches of string but the store only sells string
2 answers:
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sin2x =12/13
cos2x = 5/13
tan2x = 12/5
STEP - BY - STEP EXPLANATION
What to find?
• sin2x
,• cos2x
,• tan2x
Given:
tanx = 2/3 = opposite / adjacent
We need to first make a sketch of the given problem.
Let h be the hypotenuse.
We need to find sinx and cos x, but to find sinx and cosx, first determine the value of h.
Using the Pythagoras theorem;
hypotenuse² = opposite² + adjacent²
h² = 2² + 3²
h² = 4 + 9
h² =13
Take the square root of both-side of the equation.
h =√13
This implies that hypotenuse = √13
We can now proceed to find the values of ainx and cosx.
Using the trigonometric ratio;
And we know that tanx =2/3
From the trigonometric identity;
sin 2x = 2sinxcosx
Substitute the value of sinx , cosx and then simplify.
Hence, sin2x = 12/13
cos2x = cos²x - sin²x
Substitute the value of cosx, sinx and simplify.
Hence, cos2x = 5/13
tan2x = 2tanx / 1- tan²x
OR
Hence, tan2x = 12/5
Therefore,
sin2x =12/13
cos2x = 5/13
tan2x = 12/5
Answer: option c.
Step-by-step explanation:
You need to remember the identity:
The inverse of the tangent function is arctangent. You need to use this to calculate the angle "R":
You know that you need to find the measure of "R" and (which is the opposite side) and
(which is the adjacent side), you can sustitute values into
Then, you get: