Cotangent

If the angle α is acute, and cotan α = 1/3. Determine the value of sin α, cos α, tg α.

Correct answer:

sin α =  0.95
cos α =  0.32
tg α =  3

Step-by-step explanation:

$$\begin{gathered} cotg\alpha ={\displaystyle \frac{\cos \alpha }{\sin \alpha }} \\ \sin \alpha ={\displaystyle \frac{3}{\sqrt{1^2+3^2}}}=0.95 \end{gathered}$$

$\cos \alpha ={\displaystyle \frac{1}{\sqrt{1^2+3^2}}}=0.32$

$tg\alpha ={\displaystyle \frac{1}{cotg\alpha }}={\displaystyle \frac{3}{1}}=3$

Try another example

Related math problems and questions:

• Trigonometry
  If you know that cos(γ) = sin (806°), what is the angle γ?
• Q-Exam
  If tg α = 9.6, Calculating sin α, cos α, cotg α .
• Trigonometric functions
  In the right triangle is: ? Find the value of s and c: ? ?
• Substitution method
  Solve goniometric equation: sin⁴ θ - 1/cos² θ=cos² θ - 2
• Right triangle trigonometrics
  Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
• Cuboid
  Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°
• Regular 5-gon
  Calculate the area of the regular pentagon with side 7 cm.
• Cosine
  The point (3, 4) is on the terminal side of angle θ. cos θ = ?
• Right
  Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
• Sines
  In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
• Steeple
  We see the church tower from the road at an angle of 52°. When we zoom out to 29 meters away, it can be seen at an angle of 21°. How high is it?
• Mast
  Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 13.3°. Determine the height of the mast, if the sun above the horizon is at angle 45°12'.
• Road
  The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
• Sinus
  Determine the smallest integer p for which the equation 4 sin x = p has no solution.
• Isosceles triangle 10
  In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles.
• Tree
  Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree?
• Building
  How high is the building that throws horizontal shadow 95.4 m long at angle 50°?