Look at the figure: an image of a right triangle is shown with an angle labeled x.
if tan x° = j divided by 11 and sin x° = j divided by k, what is the value of cos x°?

cos x° = 11k
cos x° = 11j
cos x° = k divided by 11
cos x° = 11 divided by k

cos x° = 11 divided by k

Explanation:

Basic trigonometric identities are connected through a simple equation; tan x°=sin x°/cos x°, or speaking in letters: tangent of an angle is equal to the sine of that angle divided by the cosine of the same angle. So, in this case:

sin x° = j/k

tan x° = j/11

cos x° =?

Since tan x° = sin x°/cos x° that means that cos x° = sin x°/ tan x°

cos x° = j/k divided by j/11 which is equal to 11/k.

when 25.0 ml of 0.700 mol/l naoh was mixed in a calorimeter with 25.0 ml of 0.700 mol/l hcl, both initially at 20.0 °c, the temperature increased to 22.1 °c. the heat capacity of the calorimeter is 279 j/°c.

the equation for the reaction is:

naoh + hcl → nacl + h₂o

moles of hcl = 0.0250 l hcl ×

0.700

mol hcl

1 l hcl = 0.0175 mol hcl

volume of solution = (25.0 + 25.0) ml = 50.0 ml

mass of solution = 50.0 ml soln ×

1.00

ml soln

= 50.0 g soln

δt=t2-t1

= (22.1 – 20.0) °c = 2.1 °c

the heats involved are

heat from neutralization + heat to warm solution + heat to warm calorimeter = 0

q1+q2+q3=0

nδh+mcδt+cδt=0

0.0175 mol ×

δh

+ 50.0 g × 4.184 j·g⁻¹°c⁻¹ × 2.1 °c + 279 j°c⁻¹ × 2.1 °c = 0

0.0175 mol ×

δh

+ 439.32 j + 585.9 j = 0

0.0175 mol ×

δh

= -1025.22 j

δh=1025.22j0.0175 mol= -58 600 j/mol = -58.6 kj/mol