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We can see that the range will be maximum when the value of is the highest (i.e. when it is equal to 1). Clearly, 2 θ {\displaystyle 2\theta } has to be 90 degrees. That is to say, θ {\displaystyle \theta } is 45 degrees.
The range and the maximum height of the projectile do not depend upon its mass. Hence range and maximum height are equal for all bodies that are thrown with the same velocity and direction. The horizontal range d of the projectile is the horizontal distance it has traveled when it returns to its initial height ( y = 0 {\textstyle y=0} ).
Some slide rules, such as the K&E Deci-Lon in the photo, calibrate to be accurate for radian conversion, at 5.73 degrees (off by nearly 0.4% for the tangent and 0.2% for the sine for angles around 5 degrees). Others are calibrated to 5.725 degrees, to balance the sine and tangent errors at below 0.3%.
A geometric way of deriving the sine or cosine of 45° is by considering an isosceles right triangle with leg length 1. Since two of the angles in an isosceles triangle are equal, if the remaining angle is 90° for a right triangle, then the two equal angles are each 45°.
Two angles whose sum is π/2 radians (90 degrees) are complementary. In the diagram, the angles at vertices A and B are complementary, so we can exchange a and b, and change θ to π/2 − θ, obtaining: (/) =
The azimuth angle (or longitude) of a given position on Earth, commonly denoted by λ, is measured in degrees east or west from some conventional reference meridian (most commonly the IERS Reference Meridian); thus its domain (or range) is −180° ≤ λ ≤ 180° and a given reading is typically designated "East" or "West".
Below is the table of the vertex numbers for the best-known graphs (as of June 2024) in the undirected degree diameter problem for graphs of degree at most 3 ≤ d ≤ 16 and diameter 2 ≤ k ≤ 10. Only a few of the graphs in this table (marked in bold) are known to be optimal (that is, largest possible).
In everyday digital cameras, the crop factor can range from around 1, called full frame (professional digital SLRs where the sensor size is similar to the 35 mm film), to 1.6 (consumer SLR), to 2 (Micro Four Thirds ILC), and to 6 (most compact cameras). So, a standard 50 mm lens for 35 mm film photography acts like a 50 mm standard "film" lens ...