Question

Sin альфа = 0,25. Найти cos альфа и tg альфа

Answer 1

sin²α+cos²α = 1                 0.25² =  0.0625 = $\frac{1}{16}$

cosα = ±√1-sin²α

cosα = ±√1- $\frac{1}{16\\}$

cosα = ± $\frac{\sqrt{15}}{4}$

tgα = $\frac{1}{4}$ : $\frac{\sqrt{15} }{4}$ = $\frac{\sqrt{15}}{15}$     ИЛИ   tgα = $\frac{1}{4}$ : - $\frac{\sqrt{15} }{4}$ = - $\frac{\sqrt{15}}{15}$  

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Answer 2

To find the values of cosine (cos) and tangent (tg) of alpha (α) when sin alpha is given, we can use the Pythagorean trigonometric identity:

sin^2(alpha) + cos^2(alpha) = 1

Given that sin(alpha) = 0.25, we can plug this value into the equation above to find cos(alpha):

0.25^2 + cos^2(alpha) = 1

0.0625 + cos^2(alpha) = 1

Now, isolate cos^2(alpha) on one side of the equation:

cos^2(alpha) = 1 - 0.0625

cos^2(alpha) = 0.9375

Now, take the square root of both sides to find cos(alpha):

cos(alpha) = √(0.9375) ≈ 0.9682

Now that we have the value of cos(alpha), we can find tg(alpha) (tangent) using the relationship:

tg(alpha) = sin(alpha) / cos(alpha)

tg(alpha) = 0.25 / 0.9682 ≈ 0.2584

So, the values are approximately: cos(alpha) ≈ 0.9682 tg(alpha) ≈ 0.2584