Show that tan (45°) = 1
1 answer:
Answer:
Geometric proof in the explanation.
Step-by-step explanation:
Draw a square. A square has all equal sides and it's 4 angles each measure 90 degrees.
Draw a diagonal which will cut the square into two congruent isosceles right triangles.
So this will give you a 45-45-90 triangle.
I drew the triangle in the picture.
Tangent is opposite over adjacent so we don't need to find the hypotenuse in terms of a ( a is positive).
So tan(45)=a/a=1.
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SOLUTION
Write out the equation
To solve this system of equation, the aprropriate method will be substitution
Substitute the expression for y into the second equation for y, we have
Expand the paranthesis we have
Divide both sides by 4, we have
Since the value of x has been obtained, we substitute into the first equation
Therefore
x = -3, y= -4