Question

Sendo cos X =3/4 determine as demais relações trigonométricas.

Answer 1

Sabe-se que pela forma fundamental da trigonometria
cos²x + sen²x = 1
logo temos
.
sen²x = 1 - cos²x
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Substituindo cosx = 3/4 temos
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sen²x = 1 - (3/4)²
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sen²x = 1 - 9/16
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sen²x = (16 - 9)/16
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sen²x = 7/16
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senx = √(7/16)
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senx = √7 / 4
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tagx = senx / cosx
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tagx = (√7/4)/(3/4)
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tagx = √7 / 3
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cotgx = cosx/senx
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cotgx = (3/4) / (√7 /4)
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cotgx = 3/√7
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cotgx = 3√7 / 7
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secx = 1/cosx
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secx = 1/(3/4)
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secx = 4/3
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cossecx = 1/senx
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cossecx = 1 / (√7/4)
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cossecx = 4/√7
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cossecx = 4√7/7

Answer 2

Sabe-se que pela forma fundamental da trigonometria<br>cos²x + sen²x = 1<br>logo temossen²x = 1 - cos²x<br>.<br>Substituindo cosx = 3/4 temos<br>.<br>sen²x = 1 - (3/4)²<br>.<br>sen²x = 1 - 9/16<br>.<br>sen²x = (16 - 9)/16<br>.<br>sen²x = 7/16<br>.<br>senx = √(7/16)<br>.<br>senx = √7 / 4<br>.<br>tagx = senx / cosx<br>.<br>tagx = (√7/4)/(3/4)<br>.<br>tagx = √7 / 3<br>.<br>.<br>cotgx = cosx/senx<br>.<br>cotgx = (3/4) / (√7 /4)<br>.<br>cotgx = 3/√7<br>.<br>cotgx = 3√7 / 7<br>.<br>.<br>secx = 1/cosx<br>.<br>secx = 1/(3/4)<br>.<br>secx = 4/3<br>.<br>.<br>cossecx = 1/senx<br>.<br>cossecx = 1 / (√7/4)<br>.<br>cossecx = 4/√7<br>.<br>cossecx = 4√7/7