write sin 33 in terms of cosine You can express the sine function in terms of cosine without doing much work Starting with the Pythagorean identity involving sin and cos subtract cos 2 from each side and take the square root of each side
Exact Form sin 33 sin 33 Decimal Form 0 54463903 0 54463903 Free math problem solver answers your algebra geometry trigonometry calculus and statistics homework questions with step by step explanations just like a math tutor Answer Step by step explanation We are given to write sin 33 in terms of cosine We know that The sine of any acute angle is equal to the cosine of its complement Now the complement of an acute angle with measurement 33 is given by Therefore the sine of an angle with measurement 33 is equal to the cosine of an angle with
write sin 33 in terms of cosine
write sin 33 in terms of cosine
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Euler s Exponential Values Of Sine And Cosine Exponential Values Of
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Answer C Step by step explanation a a cosine and sine have to add up to 90 so subtracting 33 from 90 gives you 57 your answer would be cosine 57 Explanation For sin 33 degrees the angle 33 lies between 0 and 90 First Quadrant Since sine function is positive in the first quadrant thus sin 33 value 0 5446390 Since the sine function is a periodic function we can represent sin 33 as sin 33 degrees sin 33 n 360 n Z sin 33 sin 393 sin 753 and so on
Solved example of express in terms of sine and cosine frac 1 tan left x right 1 tan left x right 1 tan x 1 tan x Applying the tangent identity displaystyle tan left theta right frac sin left theta right cos left theta right tan cos sin A B sin C A C sin B 5 sin 33 A C sin 67 5 sin 67 sin 33 A C 8 45 A C
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Sin 33 degrees 1 2 cos 3 degrees 3 2 sin 3 degrees 1 2 0 08716 3 2 0 08716 0 04358 0 07569 0 11927 Hence using the trigonometric identities method we approximate sin 33 degrees to be approximately 0 11927 Sin 32 0 5299 cos 32 0 8480 Now let s calculate sin 2 cos 2 0 5299 2 0 8480 2 0 2808 0 7191 0 9999 We get very close to 1 using only 4 decimal places Try it on your calculator you might get better results
Next we will find the cosine and sine of the reference angle cos left dfrac 6 right dfrac 3 2 sin left dfrac 6 right dfrac 1 2 We must determine the appropriate signs for x and y in the given quadrant Range codomain of a cosine is 1 cos 1 Cosine period is equal to 2 It s an even function while sine is odd which means that cos cos and Cosine definition is essential to understand the law of cosines a very useful law to solve any triangle Discover it with our law of cosines calculator
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write sin 33 in terms of cosine - Solution We know that sin2 2 sin cos We need to determine cos Let us use the sin cos formula cos 2 sin 2 1 Rewriting we get cos 2 1 sin 2 1 9 25 cos 2 16 25 cos 4 5 sin2 2 sin cos 2 3 5 4 5 24 25 Answer sin2 24 25 Example 3 Prov e cos 4a cos 2a sin 4a